Question

At $x=\frac{A}{2}$, what fraction of the mechanical energy is potential? What fraction is kinetic? Assume potential energy to be zero at mean position.

Answer 1

$E=\frac{1}{2}k{A}^2$
$U=\frac{1}{2}k{x}^2=\frac{1}{2}k{\left(\frac{A}{2}\right)}^2=\frac{1}{4}\left(\frac{1}{2}k{A}^2\right)$
$=\frac{1}{4}E$
Hence, $\frac{1}{4}$ fraction is potential energy and $\frac{3}{4}$ fraction is kinetic energy.