What Is the Time Between Beats for This Displacement Function?

[BareFootKing]

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?

 

[Simon Bridge]

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.

 

[BareFootKing]

Thank you very much for your help.