A particle of mass 'm' is executing oscillations 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 oscillations about the origin on t

1.	A particle of mass 'm' is executing oscillations 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 POSITIONS , `x=-a` `F= maomega^(2)= 3KA^(2)` `omega prop sqrt(a):. T prop (1)/(sqrt(a))` HENCE`T alpha ("amplitude")^(-1//2)`