A particle is oscillating about x=0 along x-axis. The potential energy is given by U=k|x|^{3 _{where k is a positive constant. What is the time period of the oscillations of the particle?}}

Hi,

U asked about time period os the osccilation corresponding above Eqn 

but , hre this in not the case similiar to SHM , here time period depends on Amplitude

HOW?

if u compare the dimensions of both side then, the dimension of k = [ML^-2T^-2]

                                                  T  proportional to (mass)^x(amplitude)^y(k)^z

                                                          RHS       = [M]^x[L]^y [ML^-2T^-2]^z

                                                                     LHS =[T]

                                                              => x= 1/2 , y = z = -1/2

hence the time period depends over     1/sqrt(k)

this was good qn , we welcome all ur qns nd eager to asnweer them.

GOOD LUCK FOR UR PREPARATION