A particle starts simple harmonic motion from the mean position. Its amplitude is $a$ and total energy $E$. At one instant its kinetic energy is $3E/4.$ Its displacement at that instant is
JEE MAIN 2021, Medium
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(b) $\frac{K}{E} = \frac{{\frac{1}{2}m{\omega ^2}({a^2} - {y^2})}}{{\frac{1}{2}m{\omega ^2}{a^2}}}$
$= \frac{{{a^2} - {y^2}}}{{{a^2}}} $
$= 1 - \frac{{{y^2}}}{{{a^2}}}$
So, $\frac{{\left( {\frac{{3E}}{4}} \right)}}{E} = 1 - \frac{{{y^2}}}{{{a^2}}}$
$\Rightarrow \frac{{{y^2}}}{{{a^2}}} = 1 - \frac{3}{4} = \frac{1}{4}$
$ \Rightarrow y = \frac{a}{2}$.
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