Question

The potential energy of a particle executing SHM varies sinusoidally with frequency f. The frequency of oscillation of the particle will be:

• A. $\frac{f}{2}$
• B. $\frac{f}{\sqrt{2}}$
• C. $f$
• D. $2f$

Answer 1

The correct option is A $\frac{f}{2}$

Let the displacement equation of the particle executing $SHM$ is $x=Asin(wt+\varphi )$

where $w=2\pi f^{\prime }$

Thus potential energy of the particle is given by $P.E=\frac{1}{2}k{x}^2$

$P.E=\frac{1}{2}k{A}^{2}si{n}^2(wt+\varphi )$

$P.E=\frac{1}{2}k{A}^2[\frac{1-cos2wt}{2}]$

$⟹$ $P.E=\frac{1}{4}k{A}^2-\frac{1}{4}k{A}^{2}cos2wt$

Thus the particle oscillates at a frequency half than that of varying potential energy.

Given that P.E oscilates at frequency $f$ $⟹$ frequency of oscillation of the particle $f^{\prime }=\frac{f}{2}$