Particle motion of P consists of a periodic oscillation

[Benzoate]

Homework Statement

A particle P of mass m moves on the x-axis under the force field with potential energy V=V₀(x/b)⁴, where V₀ and b are positive constants. Show that any motion of P consists of a periodic oscillation with centre at the origin. Show further that, when oscillation has amplitude a, the period tau is given by

tau=2sqrt(2)*(m/V0)^(.5)*((b^2)/a)\int d\varsigma/(1-\varsigma^4])^.5), interval is : 0\leqx\leq1

Homework Equations

The Attempt at a Solution

Not really sure what equation I am supposed to derived.

since the problem mentions motion, I should probably start off with the equation for motion

dx/dt=+[2(E-V(x))]^.5

dx/dt=-[2(E-V(x))]^.5

 

[Benzoate]

Maybe I should rephrase the question : Anybody having trouble reading my OP?