A body of mass m is situated in a potential field `U(x)=U_(0)(1-cosalphax)` when `U_(0)` and `alpha` are constant. Find the time period of small oscialltions.

Options

A. `2pi sqrt((M)/(U_(0) alpha^(2)))`
B. `2pi sqrt((U_(0))/(M alpha^(2)))`
C. `2pi sqrt(MU_(0) alpha^(2))`
D. `2pi sqrt((U_(0)alpha^(2))/(M))`

Answer

A

Explanation

`F =- (dU)/(dx)`
`F =-(d)/(dx)(U_(0) - U_(0) cos alpha x)`
`F =-U_(0) alpha^(2)x =-kx" "T = 2pi sqrt((M)/(K))`
`T = 2pi sqrt((M)/(U_(0) alpha^(2)))`