Question

A particle is executing S.H.M with a frequency 'f', the frequency with which is K.E. oscillates is?

• A. f
• B. $f/2$
• C. $2f$
• D. $4f$

Answer 1

The correct option is C $2f$

If its frequency is $f$. Then,

let $x=A\sin (2nft+\varphi )$

$\frac{dx}{dt}=v2nfA\cos (2\pi ft+\varphi )$

so, $KE=\frac{m{v}^2}{2}\frac{m}{2}\left[2nfA\cos \right(2nft+\varphi ){]}^2$

$KE=\left(2m{\pi }^2{f}^2{A}^2{)}^2\cos \right(2nft+\varphi )$

$KE=2m{\pi }^2{f}^2{A}^2\left[\frac{1+\cos (4nft+2\varphi )}{2}\right]$

$KE=m{\pi }^2{f}^2{A}^2[1+\cos /4nft+2\varphi ]$

so, the frequency of $KE$ is

coefficient of $t$ in the expression of $KE/2n$

$=\frac{4\pi f}{2\pi }=2f$

option $C$ is correct