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"The function x = (2.5 m) cos[(4π rad/s)t + π/2 rad] gives the simple harmonic motion of a body. Find the following values at t = 5.0 s. "

(a) the displacement m

(b) the velocity (Include the sign of the value in your answer.) m/s

(c) the acceleration (Include the sign of the value in your answer.) m/s2

(d) the phase of the motion rad

(e) the frequency of the motion Hz

(f) the period of the motion

I tried:

3.14 / 2 = 1.57

Then, 4 * 3.14 = 12.56. Then, 12.6*5 = 62.8

Add both: 64.4

Apply cos in rad = 0.002

Times 2.5 = 0.08160899570341

But it says that's wrong. Am I missing something??

user442847
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1 Answers1

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The error comes from the fact that you have used the approximation $\pi \approx 3.14$ in your intermediate calculations. The rounding error is causing an error in the final answer. You can do this problem fairly easily without rounding.

$$ \cos\left (4\pi\cdot5 + \frac{\pi}{2} \right) = \cos\left (\frac{41\pi}{2} \right) = \cos\left (\frac{\pi}{2} \right) $$

Can you take it from here?

wgrenard
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