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Question

(A) In a simple harmonic motion $(SHM)$,the total mechanical energy $E$ remains constant.Total energy $E = K + U$,where $K$ is kinetic energy and $U$

Vedclass · Accepted Answer

$K_0$

Vedclass · Answer

(A) In a simple harmonic motion $(SHM)$,the total mechanical energy $E$ remains constant.Total energy $E = K + U$,where $K$ is kinetic energy and $U$ is potential energy.The kinetic energy is given as $K = K_0 \cos^2 \omega t$.The maximum value of kinetic energy $K_{\max}$ occurs when $\cos^2 \omega t = 1$,so $K_{\max} = K_0$.At the extreme positions of $SHM$,the kinetic energy is zero,and the potential energy is at its maximum.Since the total energy $E$ is equal to the maximum kinetic energy,$E = K_{\max} = K_0$.At the extreme position,$K = 0$,therefore $U_{\max} = E = K_0$.Thus,the maximum value of potential energy is $K_0$.

For a particle executing simple harmonic motion,the kinetic energy $K$ is given by $K = K_0 \cos^2 \omega t$. The maximum value of potential energy is

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