Circular and simple harmonic motion

AI Thread Summary
The discussion revolves around calculating the maximum acceleration of a vibrating structural beam in a spacecraft, given its amplitude and frequency. The amplitude is 0.25 mm, and the beam vibrates at 110 vibrations per second. Participants are trying to derive the maximum acceleration using the formula -Aw²cos(wt), where they recognize that the maximum value of cos(wt) is 1. The conversation emphasizes simplifying the problem by focusing on the constants and understanding the maximum value of the cosine function. Ultimately, the goal is to express the maximum acceleration as a multiple of gravitational acceleration, g.
AcidicVision
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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.


Homework Equations



I think...

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

The Attempt at a Solution



I don't even know where to begin. None of the problems I have done already have looked like this. I've either been given a specific time, mass or speed to work with. Would appreciate help getting started and working through this problem.
 
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AcidicVision said:
-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 don't have a value for t. Do I estrapolate it from something else?
 
AcidicVision said:
so I start with cos(110 * t). But I don't 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?
 
AcidicVision said:
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?
 
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