A particle is executing Simple Harmonic Motion $(SHM)$. The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
JEE MAIN 2023, Medium
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$x =\frac{ A }{2}, \quad \text { P.E. }=\frac{1}{2} kx ^2$
$K . E .=\frac{1}{2} kA ^2-\frac{1}{2} kx ^2$
$\frac{ P . E }{ K . E }=\frac{ x ^2}{ A ^2- x ^2}=\frac{ A ^2}{4\left(\frac{3 A ^2}{4}\right)}=\frac{1}{3}$
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