# Circular and simple harmonic motion

## Homework Statement

A vibrating strutural beam in a spacecraft can cause problems if the frequency of vibration is fairly high. Even if the amplitude of vibration is only a fraction of a millimeter, the acceleration can be several times greater than acceleration due to gravity. As an example, find the maximum acceleration of a beam that vibrates with an amplitude of 0.25mm at a rate of 110 vibrations per second. Give your awnser as a multiple of g.

I think...

-Aw^2cos(wt)
w = 2pi/T

## The Attempt at a Solution

I dont even know where to begin. None of the problems I have done already have looked like this. Ive either been given a specific time, mass or speed to work with. Would appreciate help getting started and working through this problem.

## Answers and Replies

Hootenanny
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Science Advisor
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-Aw^2cos(wt)
w = 2pi/T
That looks good to me. So you want to find the maximum value of -Aw2cos(wt). Now, A and w are constants so you can just ignore them, so what you really need to know it the maximum value of cos(wt).

so I start with cos(110 * t). But I dont have a value for t. Do I estrapolate it from something else?

Hootenanny
Staff Emeritus
Science Advisor
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so I start with cos(110 * t). But I dont have a value for t. Do I estrapolate it from something else?
Think simpler than that, what is the maximum value which cos(x) can take?

0.25 would be max and -0.25 would be min with an origin point in the middle?

Hootenanny
Staff Emeritus
Science Advisor
Gold Member
0.25 would be max and -0.25 would be min with an origin point in the middle?
I'm sorry, but I have no idea what you mean. Try sketching a graph of y=cos(x), what is the maximum value of this curve, i.e. what is the largest value of y?