Question

A particle of mass $m$ is executing SHM about the origin on $x$ -axis with frequency $\sqrt{\frac{k a}{\pi m}}$, where $k$ is a constant and $a$ is the amplitude. Find its potential energy, if $x$ is the displacement at time $t$ :

• A. $k a x^{2}$
• B. $k a^{2} x$
• C. $2 \pi k a x^{2}$
• D. $2 \pi k x^{3}$

Answer 1

Answer: (C)

$2 \pi f=\omega ; 2 \pi \sqrt{\frac{k a}{\pi m}}=\omega$
Potential energy $U=\frac{1}{2} m \omega^{2} x^{2}=2 \pi kax ^{2}$