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## Homework Statement

Assume that the potential is symmetric with respect to zero and the system has amplitude ##a##, show that the period is given by : ##T=\sqrt{8m}\int^a_0\frac{dx}{\sqrt{V(a)-V(x)}}.##

## Homework Equations

##E = \frac12 m(\frac{dx}{dt})^2+V(x)##

## The Attempt at a Solution

For a particle, I know that at ##t=0## if we release it from rest at position ##x=a## we then have ##\frac{dx}{dt}=0## at ##t=0## and thus ##E=V(a)##. So when the particle reaches the origin for the first time it has gone through one quarter of a period of the oscillator. Thus, I have to integrate with respect to t from ##0## to ##\frac{T}{4}## and rearrange the equation ##E## for ##\frac{dx}{dt}##. But from here I am not sure how to set it up properly to get ##T=\sqrt{8m}\int^a_0\frac{dx}{\sqrt{V(a)-V(x)}}.##