chapter 13: oscillations about equilibrium whenever f = -kx or u(x) is a parabola u = kx 2 /2 f =...

Chapter 13: Oscillations About Equilibrium

Whenever F = -kx or U(x) is a parabola

U = kx2/2

F = -kx

Ch13-1 Periodic Motion

T = period – the time for one cycle or repeat time

f = frequency – the number of cycles per second

f = 1/T

= angular frequency – radians per second

= 2f = 2/T

Don’t confuse angular frequency with angular velocity.


Ch13-2 Simple Harmonic Motion (SHM)




Displaying Position Versus Time for Simple Harmonic Motion

t = 0x = Acos(2t/T)



Simple Harmonic Motion as a Sine or a Cosine


P13.8 (p.425)


CT1: A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below. At point P, the mass has

A. positive velocity and positive acceleration.

B. positive velocity and negative acceleration.

C. positive velocity and zero acceleration.

D. negative velocity and positive acceleration.

E. negative velocity and negative acceleration.

F. negative velocity and zero acceleration.

G. zero velocity but is accelerating (positively or negatively).

H. zero velocity and zero acceleration.

CT2: A mass suspended from a spring is oscillating up and down as indicated. Consider two possibilities: (i) at some point during the oscillation the mass has zero velocity but is accelerating (positively or negatively); (ii) at some point during the oscillation the mass has zero velocity and zero acceleration.

A. Both occur sometime during the oscillation.B. Neither occurs during the oscillation.C. Only (i) occurs.D. Only (ii) occurs.

Ch13-3 Connections Between Uniform Circular Motion and SHM




Position Versus Time in Simple Harmonic Motion



Velocity Versus Time in Simple Harmonic Motion



Acceleration Versus Time in Simple Harmonic Motion


P13.22 (p.425)


P13.66 (p.428)

Ch13-4 The Period of a Mass on a Spring

P13.63 (p.427)


P13.31 (p.426)

k

m1

Factors Affecting the Motion of a Mass on a Spring

Ch13-5 Energy Conservation in Oscillatory Motion

E = mv2/2 + kx2/2 = kA2/2 = mvmax2/2 = mA22/2



U = kA2cos2t/2 K = mA22sin2t/2 = kA2sin2t/2



P13.67 (p.428)


CT3: In P13.67b, which principle do we have to use to get the speed of the bob and bullet right after the collision?

A. Newton’s laws.

B. Conservation of energy.

C. Conservation of momentum.

D. The work-kinetic energy theorem.

CT4: In P12.67b, which principle do we have to use to get the speed of the bullet from the height the bob rises?

A. Newton’s laws.

B. Conservation of energy.

C. Conservation of momentum.

D. The work-kinetic energy theorem.

Ch13-6 Simple Pendulum


Ch13-6 Simple Pendulum

P13.67c (p.428)


CT5: In P13.52a the acceleration of gravity at the surface of the Moon is one-sixth that at the surface of the Earth. If the pendulum were taken to the Moon, the period will

A. increase.

B. decrease.

C. stay the same.

Simple Pendulum: Energy View

Ch13-7 Damped Oscillations


Ch13-8 Driven Oscillations and Resonance


chapter 13: oscillations about equilibrium whenever f = -kx or u(x) is a parabola u = kx 2 /2 f =...

Documents

equilibrium slide

simple harmonic motion

equilibrium velocity

kx slide

spring slide

equilibrium acceleration

cosine slide

acos2tt slide