A particle attached to a spring is executing simple harmonic motion. The motion

Question

A particle attached to a spring is executing simple harmonic motion. The motion is described by the equation:
x(t)= 4.0 m cos(2 pi t)
State which of the following statements are true, which are not true and explain why
a. At the maximum and minimum values of the displacement, the velocity is zero
b. At the maximum and minimum values of the displacement, the acceleration is zero
c.When the displacement is zero, the velocity is zero
d. When the displacement is zero, the acceleration is zero
e. The period of this motion is 2 s.
f.The amplitude of this motion is 2.0 m

Explanation / Answer

a. True. As you approach maximum displacement, you travel slower and slower -- the maximum is that point where you finally come to a halt and begin to reverse.

b. False. As above, your acceleration is increasing in magnitude (trying to pull you back) as you extend, reaching a maximum at maximum displacement.

c. False. That is when you are moving fastest, swinging through the zero point.

d. True. At the zero point, you are coasting on your high velocity and acceleration doesn't begin again until you pull away from zero.

e. False. Period is 1 sec. T = 2/ and we see that = 2. Another way to look at it, every second you come full circle, the cosine function is all the way back to 2.

f. False. Amplitude is 4.0 m, the leading coefficient.

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