Question

A pendulum is undergoing SHM with frequency $f$ . What is the frequency of its kinetic energy?

• A. f/2
• B. 2f
• C. 3f
• D. 4f

Answer 1

Answer: (B)

Let, $x=A\sin \omega t$
$v=\frac{dx}{dt}=A\omega \cos \omega t$
Kinetic energy, $K=\frac{1}{2}m{v}^2$
$\Rightarrow K=\frac{1}{2}m{\omega }^2{A}^2{\cos }^2\omega t$
$\Rightarrow K=\frac{1}{2}m{\omega }^2{A}^2\left(\frac{1+\cos 2\omega t}{2}\right)$
$\Rightarrow K=\frac{1}{4}m{\omega }^2{A}^2\left(1+{\cos }^2\omega t\right)$
$\therefore {\omega }_K=2\omega$
$\therefore$ Frequency of oscillation of $K\cdot E=2f\left[f=\frac{\omega }{2\pi }\right]$