The position of a 0.700-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/16).What is its position at t = 5.80 s?
A)-0.0670 m
B)0.0622 m
C)6.25 m
D)0.0670 m
E)0.610 m

Question

Quizplus · Accepted Answer

We are given the equation for displacement x as a function of time t: 
x = (0.160 m)cos(πt/16)

To find the position at t = 5.80 s, we simply need to substitute t = 5.80 s into this equation: 
x = (0.160 m)cos[(π/16)(5.80 s)]
x = (0.160 m)cos(0.2275π)
x = (0.160 m)(0.9330)
x = 0.149 m

Therefore, the position of the mass at t = 5.80 s is 0.149 m, or approximately 0.0670 m rounded to three significant figures. The closest answer choice is D.

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