Total energy \(=\frac{1}{2} m \omega^2 a^2\) and

kinetic energy when displacement is \((x)\)

\(K=\frac{1}{2} m \omega^2\left(a^2-x^2\right)\)

\(=\frac{1}{2} m \omega^2\left(a^2-\left(\frac{a}{2}\right)^2\right)=\frac{3}{4}\left(\frac{1}{2} m \omega^2 a^2\right)\)

Therefore fraction of the total energy at \(x\) is

\(=\frac{\frac{3}{4}\left(\frac{1}{2} m \omega^2 a^2\right)}{\frac{1}{2} m \omega^2 a^2}=\frac{3}{4}\)