What Is the Time Between Beats for This Displacement Function?

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SUMMARY

The displacement function for a mass is defined as x = 3cos((10π)t) + 3cos((11π)t). To determine the time between beats, which corresponds to the time between maximum displacements, the derivative of the function is taken and set to zero, resulting in the equation 10sin((10π)t) + 11sin((11π)t) = 0. The solution involves finding the beat frequency, which is the difference between the two frequencies, leading to a time between beats calculated as one over the beat frequency. The envelope function's period is crucial for solving this problem.

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Homework Statement


The displacement of a mass as a function is given by the equation

x = 3cos((10pi )t) + 3cos((11\pi)\t)

What is the time between beats, i.e the time between occurrence of the maximum displacement?

Homework Equations



At a maximum v = 0

The Attempt at a Solution



I took the derivative of the function and set it equal to zero
10sin((10pi)t) + 11sin((11pi)t) = 0

I can't find an analytical way of solving this problem. I have tried various trig identities , expanding the functions which took an hour but go no where. Is my strategy of finding the zeros this way the right one or should I come up with a different strategy. And if the latter than where should I start from?
 
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You want the period of the envelope function.
http://en.wikipedia.org/wiki/Beat_(acoustics )

The time between beats would be one over the beat frequency.
 
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Thank you very much for your help.
 

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