Circular and simple harmonic motion

1. Nov 20, 2008

AcidicVision

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

I think...

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

3. 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.

2. Nov 20, 2008

Hootenanny

Staff Emeritus
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).

3. Nov 20, 2008

AcidicVision

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

4. Nov 20, 2008

Hootenanny

Staff Emeritus
Think simpler than that, what is the maximum value which cos(x) can take?

5. Nov 20, 2008

AcidicVision

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

6. Nov 20, 2008

Hootenanny

Staff Emeritus
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?