Question

In SHM, for how many times potential energy is equal to kinetic energy during one complete period?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

We know, total mechanical energy $E$ is conserved in SHM.
$\therefore E=U+\text{KE}$
For $U=\text{KE}$
(or) $U=\frac{E}{2}$
$\Rightarrow \frac{1}{2}m{\omega }^2{x}^2=\frac{1}{2}\left(\frac{1}{2}m{\omega }^2{A}^2\right)$
$\Rightarrow x=\pm \frac{A}{\sqrt{2}}$
For one complete cycle, particle will pass through these points $4$ times.