A particle of mass m is executing osillations about the origin on the x -axis.Its P.E. is U(x)=K|x|^(3), where k is a positive constant. If the amplitude of oscillation is a then how does its time period T vary with amplitude.

A particle of mass m is executing osillations about the origin on the

1.	A particle of mass m is executing osillations about the origin on the x -axis.Its P.E. is U(x)=K\|x\|^(3), where k is a positive constant. If the amplitude of oscillation is a then how does its time period T vary with amplitude.
Answer» Solution :`U(x)=k\|x\|^(3)""F=(dU)/(dx)=3kx^(2)` At EXTREME POSITONS `x=+-a` `F=maomega^(2)=3KA^(2)` `OMEGA prop sqrt(a)"" :. Tprop 1/(sqrt(a))` Hence `T prop ("amplitude")^(-1//2)`