A particle executes S.H.M. with amplitude A and time period T . The...

V = \omega\sqrt{{A}^{2} - {x}^{2}}{V}_\max = A\omega

$\dfrac{A\omega}{2} = \omega\sqrt{{A}^{2} - {x}^{2}}$

$\dfrac{{A}^{2}}{4} = {A}^{2} - {x}^{2}$

${x}^{2} = \dfrac{3{A}^{2}}{4}$

$x = \dfrac{\sqrt{3}}{2}A$