Oscillations – motions that repeat themselves

Period ( T ) – the time for one complete oscillation

Frequency ( f ) – the number of oscillations completed each unit of time

Units: 1 Hertz (Hz) = 1 oscillation per second

fT

1

Consider the forces acting on the mass when it is at rest.

gF

sF

gs FF

0netF

Equilibrium Position – Occurs when the net force acting upon an oscillating object is zero.

Net force acting on a mass on a

spring

Simple Harmonic Motion – the motion executed by a particle of mass m subject to a force that is proportional to the displacement of the particle but opposite in sign.

xFnet

Restoring Force – A force that acts towards the equilibrium position and results in oscillatory motion.

xkFspring

Hooke’s Law

Consider an object moving with uniform circular motion

In rotational terms, the object moves with a

constant angular velocity ω and therefore angular position θ is given by

ot

Consider the projection of the motion of this object onto the horizontal plane.

This motion appears exactly like that of a mass on the end of a spring!

r

cosr

ot

cosrx

But

0cos trtx

Simple harmonic motion is the projection of uniform circular motion on a diameter of the circle in which the circular motion occurs

r

cosr

0cos trtx

Simple harmonic motion is the projection of uniform circular motion on a diameter of the circle in which the circular motion occurs

Amplitude (xm) – the magnitude of the maximum displacement from the equilibrium position

. at object the of

ntdisplaceme the on depends it motion,

y oscillator the of point starting the

- Constant Phase AnglePhase

0t

mo xx when0

Oscillations

txtx m cos

Simple Harmonic Motion – the motion executed by a particle of mass m subject to a force that is proportional to the displacement of the particle but opposite in sign.

– periodic motion in which the position is a sinusoidal function of time

Mass on a spring

Oscillations

txtx m cos

Angular Frequency

In rotation, ω refers to the angular velocity. However, in oscillatory motion, ω is called

fT

22

srad :Units

Angular Frequency (ω) – rate of change of angular displacement of an oscillating object

tx

T 2For one complete oscillation