Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.

Definition of an Oscillating System

So what exactly is an oscillating system? In short, it is a system in which a particle or set of

particles moves back and forth. Whether it be a ball bouncing on a floor, a pendulum swinging

back and forth, or a spring compressing and stretching, the basic principle of oscillation

maintains that an oscillating particle returns to its initial state after a certain period of time. This

kind of motion, characteristic of oscillations, is called periodic motion, and is encountered in all

areas of physics.

We can also define an oscillating system a little more precisely, in terms of the forces acting on a

particle in the system. In every oscillating system there is an equilibrium point at which no net

force acts on the particle. A pendulum, for example, has its equilibrium position when it is

hanging vertical, and the gravitational force is counteracted by the tension. If displaced from this

point, however, the pendulum will experience a gravitational force that causes it to return to the

equilibrium position. No matter which way the pendulum is displaced from equilibrium, it will

experience a force returning it to the equilibrium point. If we denote our equilibrium point as x =

0 , we can generalize this principle for any oscillating system:

In an oscillating system, the force always acts in a direction opposite to the displacement of the

particle from the equilibrium point.

This force can be constant, or it can vary with time or position, and is called a restoring force. As

long as the force obeys the above principle, the resulting motion is oscillatory. Many oscillating

systems can be quite complex to describe. We shall focus on a special kind of oscillation,

harmonic motion, which yields a simple physical description. Before we do so, however, we must

establish the variables that accompany oscillation.

Variables of Oscillation

In an oscillating system, the traditional variables x , v , t , and a still apply to motion. But we must

introduce some new variables that describe the periodic nature of the motion: amplitude, period,

and frequency.

Amplitude

A simple oscillator generally goes back and forth between two extreme points; the points of

maximum displacement from the equilibrium point. We shall denote this point by x m and define it

as the amplitude of the oscillation. If a pendulum is displaced 1 cm from equilibrium and then

allowed to oscillate we can say that the amplitude of oscillation is 1 cm.