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(C) The displacement of a particle in simple harmonic motion is given by $x = a \sin(\omega t)$.The velocity is $v = \frac{dx}{dt} = a\omega \cos(\ome

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$2f$

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(C) The displacement of a particle in simple harmonic motion is given by $x = a \sin(\omega t)$.The velocity is $v = \frac{dx}{dt} = a\omega \cos(\omega t)$.The kinetic energy $K$ is given by $K = \frac{1}{2}mv^2 = \frac{1}{2}m(a\omega \cos(\omega t))^2$.Using the trigonometric identity $\cos^2 	heta = \frac{1 + \cos(2	heta)}{2}$,we get:$K = \frac{1}{2}m a^2 \omega^2 \cos^2(\omega t) = \frac{1}{4}m a^2 \omega^2 (1 + \cos(2\omega t))$.The term $\cos(2\omega t)$ indicates that the kinetic energy oscillates with an angular frequency of $2\omega$.Since $\omega = 2\pi f$,the frequency of oscillation of kinetic energy is $2f$.

Column-$I$	Column-$II$
$(a)$ $K = 10\,J$	$(i)$ $U = 40\,J$
$(b)$ $K = 60\,J$	$(ii)$ $U = 90\,J$
	$(iii)$ $U = 50\,J$

$A$ particle executes simple harmonic motion with a frequency $f$. The frequency with which its kinetic energy oscillates is

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