A particle of mass $m$ performs $SHM$ along a straight line with frequency $f$ and amplitude $A.$
Medium
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if $x=$ $Asinwt$ $\Rightarrow v=$ $Awcoswt$ $\Rightarrow v^{2}=A^{2} \times 4 \pi^{2} f^{2} \cos ^{2} \omega t=4 \pi^{2} f^{2} A^{2}(1+\cos 2 \omega t) / 2=$
$2 \pi^{2} f^{2} A^{2}(1+\cos 2 \omega t)$
The average potential energy is equal to average kinetic energy is equal to average of $m v^{2} / 2=\frac{1}{2} m \times 2 \pi^{2} f^{2} A^{2}(1+\cos 2 \omega t)-(1)$
$\Rightarrow m \pi^{2} f^{2} A^{2}$
From $( 1 ),$ angular frequency of oscillation of kinetic energy is $2$ $\omega$ i.e., frequency of oscillation of kinetic energy is $2 f$
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