A particle starts with $S.H.M.$ from the mean position as shown in the figure. Its amplitude is $A$ and its time period is $T$. At one time, its speed is half that of the maximum speed. What is this displacement?
AIPMT 1996, Medium
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(c) ${v_{\max }} = \omega A$
$v = \frac{{\omega A}}{2} = \omega \sqrt {{A^2} - {y^2}} $
${A^2} - {y^2} = \frac{{{A^2}}}{4}$
${y^2} = \frac{{3{A^2}}}{4}$
$y = \frac{{\sqrt 3 A}}{2}$
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