Question

A body of mass m is situated in a potential field U(x) = U0(1-cos αx ) when U0 and α are constants. Find the time period of small oscillations​

Answer 1

The time period of small oscillations is T = 2π √m / Uoα^2

Explanation:

The time period of small oscillations.

U = Uo ( 1- coxαx)

F = -dU / dx  = -d / dx (Uo - Uocos αx)

F = - Uoasinαx

F -Uo ααx

F = - Uoα^2x

We know that

F = - kx

So K = Uoα^2

T = 2π √m / Uoα^2

Thus the time period of small oscillations is T = 2π √m / Uoα^2

Also learn more

A pendulum osscilates 40 times in 4 seconds. Find its time period and frequency. ?

https://brainly.in/question/6767953