Question

A particle excutes SHM of frequency f. The frequency of its kinetic energy is ?

Answer 1

`2f`

Explanation:

For displacement:

• `x = A sin omega t`

Velocity is:

• `dot x = omega A cos omega t`

And Kinetic Energy is:

• `T = 1/2 m dotx^2 = 1/2 m omega^2 A^2 cos^2 omega t`

Using identity:

• `cos 2 alpha = 2 cos^2 alpha - 1`

`T = 1/2 m omega^2 A^2* (cos color(red)( 2 omega) t + 1)/2`

`T` has angular frequency `omega' = 2 omega`, and therefore frequency `f' = 2 f`, as `omega = 2 pi f`