Question

The time period of the variation of potential energy of a particle executing $SHM$ with period $T$ is

• A. $T/4$
• B. $T$
• C. $2T$
• D. $T/2$
• E. $T/3$

Answer 1

The correct option is A $T/4$

Potential energy of particle executing SHM $=\frac{1}{2}m{\omega }^2{x}^2$

The relation between $\omega$ and $T$ is given as: $T=\frac{2\pi }{\omega }or\omega =\frac{2\pi }{T}$

Put the value of $\omega$ in the potential energy expression as:

$U=\frac{1}{2}m\frac{4{\pi }^2}{T^2}{x}^2$

$=\frac{2m{\pi }^2{x}^2}{T^2}$

$U\propto \frac{1}{T^2}$