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Simple harmonic motion problem

The initial (t=0) position, velocity, and acceleration of an object moving in simple harmonic motion (with center at the origin x=0) are xi=3.00 cm, vi=4.00 cm/s, and ai=-7.00 cm/s2, respectively. Use the cosine function to specify the position.

(a) Determine the angular frequency of the motion.
rad/s

(b) Determine the frequency and period.
Hz
s

(c) Determine the phase constant.
rad (0 phase constant < 2(pie))

(d) Determine the amplitude of the motion.
cm

(e) Determine the position of the object at time t = 0.350 s.
cm

Solution Preview

Let use the cosine function to specify the position x:
x=Acos(wt+p) (1)
A=amplitude
w=angular frequency
t=time
p=phase

We also have
v=x'=-Awsin(wt+p) (2)
a=v'=x"=-Aw^2cos(wt+p) (3)

(a) Determine the angular frequency of the motion in rad/s:
Apply the initial conditions into equations (1) and ...

Solution Summary

The solution provides detailed calculations and explanations for the problem.

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