The frequency at which kinetic energy changes | vedclass

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(C) In $S.H.M.$,the displacement is given by $x = A \sin(\omega t)$.The kinetic energy is $K.E. = \frac{1}{2} m \omega^2 A^2 \cos^2(\omega t) = \frac{

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$2f$

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(C) In $S.H.M.$,the displacement is given by $x = A \sin(\omega t)$.The kinetic energy is $K.E. = \frac{1}{2} m \omega^2 A^2 \cos^2(\omega t) = \frac{1}{4} m \omega^2 A^2 (1 + \cos(2\omega t))$.The potential energy is $P.E. = \frac{1}{2} k x^2 = \frac{1}{2} k A^2 \sin^2(\omega t) = \frac{1}{4} k A^2 (1 - \cos(2\omega t))$.Both kinetic and potential energies oscillate with an angular frequency of $2\omega$.Since the frequency $f = \frac{\omega}{2\pi}$,the frequency of energy oscillation is $f' = \frac{2\omega}{2\pi} = 2f$.Therefore,the frequency at which kinetic energy changes into potential energy is $2f$.

The frequency at which kinetic energy changes into potential energy in a simple harmonic motion ($S$.$H$.$M$.) with frequency $f$ is:

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