For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

(3)

$\mathrm{KE}=\mathrm{PE}$

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

$A^{2}-x^{2}=x^{2}$

$2 x^{2}=A^{2}$

$\mathrm{x}=\pm \frac{\mathrm{A}}{\sqrt{2}}$