similarly, at extreme points, $K E=0$ and $P E=$ $max.$

so average of total energy is equal to total energy at extreme position which is maximum potential energy.

Now, if $x=A \sin \omega t \Rightarrow v=A \omega \cos \omega t$

Maximum velocity is $v_{\max }=A \omega$ and $\mathrm{rms}$ value of velocity is $A \omega / \sqrt{2}=v_{\max } / \sqrt{2}(\because \mathrm{rms}$ value of $\cos \theta$ is $1 / \sqrt{2}$ )