A body performs S.H.M. Its kinetic energy K v | vedclass

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(A) For a body performing $S.H.M.$,the displacement is given by $x = A \sin(\omega t + \phi)$.The velocity is $v = \frac{dx}{dt} = A\omega \cos(\omega

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(A) For a body performing $S.H.M.$,the displacement is given by $x = A \sin(\omega t + \phi)$.The velocity is $v = \frac{dx}{dt} = A\omega \cos(\omega t + \phi)$.The kinetic energy $K$ is given by $K = \frac{1}{2}mv^2 = \frac{1}{2}m A^2 \omega^2 \cos^2(\omega t + \phi)$.Using the identity $\cos^2 	heta = \frac{1 + \cos(2	heta)}{2}$,we get $K = \frac{1}{4}m A^2 \omega^2 [1 + \cos(2\omega t + 2\phi)]$.This shows that the kinetic energy $K$ varies with time $t$ with a frequency double that of the $S.H.M.$ and is always non-negative $(K \ge 0)$.Graph $A$ shows a periodic variation where $K$ is always non-negative,which matches the derived expression.

$A$ body performs $S.H.M.$ Its kinetic energy $K$ varies with time $t$ as indicated by which graph?

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