Question : A particle moves in a force field given by the potential $V(x) = A |x|^n $  Find the time period as function of energy. 

 Answer:  $T= \left\{\displaystyle {2\over n}\sqrt{2m\pi\over E} {\left(E\over A\right)^{1/n}{\Gamma(1/n)\over \Gamma({n+2\over 2n})}}\right\}$