Question

A particle executes simple harmonic motion with a frequency ${}^{\prime }{f}^{\prime }$. The frequency with which its kinetic energy oscillates is?

• A. $\frac{f}{2}$
• B. $f$
• C. $2f$
• D. $4f$

Answer 1

The correct option is C $2f$

Let, $x=A\sin \omega t$

$v=\frac{dx}{dt}=A\omega \cos \omega t$

Kinetic energy, $K=\frac{1}{2}m{v}^2$

$⟹K=\frac{1}{2}m{\omega }^2{A}^2{\cos }^2\omega t$

$⟹K=\frac{1}{2}m{\omega }^2{A}^2\left(\frac{1+cos2\omega t}{2}\right)$

$⟹K=\frac{1}{4}m{\omega }^2{A}^2(1+{\cos }^2\omega t)$

$\therefore {\omega }_K=2\omega$

$\therefore$ Frequency of oscillation of K.E $=2f[f=\frac{\omega }{2\pi }]$