Physics - SHM Question with Solution | TestHub

The potential energy of a simple harmonic oscillator at a displacement $x$ is given by $U=\frac{1}{2}k{x}^2$.

The total energy of the oscillator is $E=\frac{1}{2}k{A}^2$.

Given the displacement $x=\frac{3}{4}A$, substituting this into the potential energy formula gives:

$U=\frac{1}{2}k{\left(\frac{3}{4}A\right)}^2$

$U=\frac{9}{16}\left(\frac{1}{2}k{A}^2\right)$

Since $E=\frac{1}{2}k{A}^2$, we get:

$U=\frac{9}{16}E$

Answer: $\frac{9}{16}E$