Ch 15 Oscillatory Motion 15-1 Motion of an Object Attached to a Spring Acos  F s = -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 Motion 15-2 A Particle in Simple Harmonic Motion x = Acos(t+)  = 2/T f = 1/T = /2 a = -  2 x

Fig. 15.6, p.458 x=Acos t=-/

Ch 15 Oscillatory Motion 15-2 A Particle in Simple Harmonic Motion P15.3 (p.441) P15.5 (p.441)

Ch 15 Oscillatory Motion 15-2 A Particle in Simple Harmonic Motion: Mass on a Spring F x = F s = -kx = ma = md 2 x/dt 2 d 2 x/dt 2 +  2 x = 0, where  2 = k/m Try x = Acos(t+) P15.4 (p.441)

Ch 15 Oscillatory Motion 15-3 Energy of the Simple Harmonic Oscillator E = kA 2 /2 = mv max 2 /2 = m(A) 2 /2 = kA 2 /2 E = kx 2 /2 + mv 2 /2 is constant P15.17 (p.441)

Fig , p.462

Ch 15 Oscillatory Motion 15-5 Pendulum and Other SHO

Fig , p.470 A. Torsion Pendulum

r t B. Simple Pendulum

Simple Pendulum: Energy View

Fig , p.469 C: Physical Pendulum P15.33 (p.443)

Ch 15 Oscillatory Motion 15-6 Damped Oscillations

Fig , p.471

Fig , p.471 overdamped critically damped underdamped

Ch 15 Oscillatory Motion 15-7 Forced Oscillations

Fig , p.473

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