A particle of mass m moves in a one dimensional potential

[AdityaDev]

1.The problem, statement, all variables and given/known data

A particle of mass m moves in a one dimensional potential U(x)=A|x|³, where A is a constant. The time period depends on the total energy E according to the relation T=E^-1/k
Then find the value of k.

2. Homework Equations

V=dx/dt
E=kinetic energy + U
F=-dU/dx

The Attempt at a Solution

$E=\frac{1}{2}mv^2+a|x|^n$
$v=\sqrt{\frac{2}{m}(E-a|x|^n)}$
$dt=\frac{dx}{v}$
Integrating LHS, I can get the time period. But when integrating RHS, how do I find the limits?

 

[ehild]

The particle moves between the turning points, where its velocity becomes zero, that is, the potential energy is equal to the total energy E.