A particle executes SHM of amplitude A . The distance from the mean...

The potential energy is given by

$U = \dfrac{m{\omega}^{2}{x}^{2}}{2}$

The kinetic energy is given by $K = \dfrac{m{\omega}^{2} ( {A}^{2} - {x}^{2} )}{2}$.

Using the condition that $K = U$,

$\dfrac{1}{2}m{\omega}^{2}\left({A}^{2} - {x}^{2}\right) = \dfrac{1}{2}m{\omega}^{2}{x}^{2}$

$⇒ x = \dfrac{A}{\sqrt{2}}$