Physics - SHM Question with Solution | TestHub

For a particle performing Simple Harmonic Motion (S.H.M.), the restoring force $F$ acting on it at a displacement $x$ is given by:

$F=-kx$

The potential energy $E$ of the particle at displacement $x$ is given by:

$E=\frac{1}{2}k{x}^2$

Dividing the expression for potential energy by the expression for restoring force, we get:

$\frac{E}{F}=\frac{\frac{1}{2}k{x}^2}{-kx}$

$\frac{E}{F}=-\frac{x}{2}$

Rearranging the terms, we obtain:

$\frac{2E}{F}=-x$

$\frac{2E}{F}+x=0$

Answer: $\frac{2\text{E}}{\text{F}}+x=0$