A particle of mass (m) is executing oscillations about the origin on the (x) axis. Its potential energy is `V(x) = k|x|^3` where (k) is a positive constant. If the amplitude of oscillation is a, then its time period (T) is.

Explanation

`U(x) = K|x|^(3)`, but `U = (1)/(2) mA^(2) omega^(2) sin^(2) omegat`
`ma^(2) omega^(2) prop Ka^(3) rArr omega prop sqrt(a)` and `T prop (1)/(sqrt(a))`