Ch 15 Oscillatory Motion15-1 Motion of an Object Attached to a Spring

Acos

Fs = -kx

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.

Ch 15 Oscillatory Motion15-2 A Particle in Simple Harmonic Motion

x = Acos(t+) = 2/T f = 1/T = /2

a = - 2x

Fig. 15.6, p.458

x=Acos

t=-/

Ch 15 Oscillatory Motion15-2 A Particle in Simple Harmonic Motion

P15.3 (p.441)

P15.5 (p.441)

Ch 15 Oscillatory Motion15-2 A Particle in Simple Harmonic Motion: Mass on a Spring

Fx = Fs = -kx = ma = md2x/dt2

d2x/dt2 + 2x = 0, where 2 = k/m

Try x = Acos(t+)

P15.4 (p.441)

Ch 15 Oscillatory Motion15-3 Energy of the Simple Harmonic Oscillator

E = kA2/2 = mvmax2/2 = m(A)2/2 = kA2/2

E = kx2/2 + mv2/2 is constant

P15.17 (p.441)

Fig. 15.10, p.462

Ch 15 Oscillatory Motion15-5 Pendulum and Other SHO

Fig. 15.20, p.470

A. Torsion Pendulum

rt

B. Simple Pendulum

Simple Pendulum: Energy View

Fig. 15.18, p.469

C: Physical Pendulum

P15.33 (p.443)

Ch 15 Oscillatory Motion15-6 Damped Oscillations

Fig. 15.22, p.471

Fig. 15.23, p.471

overdamped

criticallydamped

underdamped

Ch 15 Oscillatory Motion15-7 Forced Oscillations

Fig. 15.25, p.473

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