tion 13-8 The position versus time graph for a simple harmonic oscillator is sho
ID: 1773597 • Letter: T
Question
tion 13-8 The position versus time graph for a simple harmonic oscillator is shown in Figure 13-49, Time Plots for Simple Harmonic Motion 59. What are the amplitude and the period? (b) What is the phase constan (c) What is the phase at 1 s andi 2 s? (d) Write an equation for the oscillator that describes its (a) What are the amplitud (b) What is the equilibriun (c) What is the phase con (d) Write an equation for position a(t) as a fund point x = 0 position x(t) as a function of time. (e) What is the velocity of the oscillator at t= 1.0 s? () What is the acceleration of the oscillator at t 2 s? e) Write an equation for is /2 rad out of phase (1) What is the acceleratic 0.8 1.3 0.6 1.2 1.01 0.9 0.8 0.7 0.2 E 0.0 -0.2 -0.4 0.6 -0.8 0.5 1 /5 2 2.5 3 3.5 4 ·5 5 Figure 13-51 Problem 61 t (s) Figure 13-49 Problem 59 62. The position versus The velocity versus time graph for a simple har- hown monic oscillator is shown in Figure 13-50. (a) What are the maximum speed and the period? b) What is the amplitude? in Figure 13-52. (a) What is the phase diff tors at 1 = 1.0 s? 60. (b) At what times, closest t have zero velocities?Explanation / Answer
59)a) amplitude A = 0.6 m
period T = 3 s
b) phase constanr = pi
c) phase at t=1 s. is -pi/3 or 5pi/3
phase at t=2s is pi/3
d]. x = 0.6 sin ((2pi/3)t + pi)
e] v = 0.6*2pi/3 cos((2pi/3)t + pi)
at t=1s, v = 0.6*2pi/3* 0.5 = 0.628 m/s
f] a = 0.6*(2pi/3)^2 sin((2pi/3)t + pi)
at t=2s, a = 0.6*(2pi/3)^2 sin (pi/3) = 2.28 m/s^2
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