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)

2f

Answer 2

Let, $x=A \sin \omega t$
$v=\frac{d x}{d t}=A \omega \cos \omega t$
Kinetic energy, $K =\frac{1}{2} mv ^{2}$
$\Rightarrow K =\frac{1}{2} m \omega^{2} A ^{2} \cos ^{2} \omega t$
$\Rightarrow K =\frac{1}{2} m \omega^{2} A ^{2}\left(\frac{1+\cos 2 \omega t }{2}\right)$
$\Rightarrow K =\frac{1}{4} m \omega^{2} A ^{2}\left(1+\cos ^{2} \omega t \right)$
$\therefore \omega_{ K }=2 \omega$
$\therefore$ Frequency of oscillation of $K \cdot E=2 f \left[f=\frac{\omega}{2 \pi}\right]$
So, the correct option is (B) : 2f.