Assertion (A): In S.H.M,kinetic and potential | vedclass

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(B) In $S.H.M$,the kinetic energy $(K.E)$ and potential energy $(P.E)$ are given by:$K.E = \frac{1}{2} m \omega^2 (a^2 - y^2)$$P.E = \frac{1}{2} m \om

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$A$ and $R$ are true. $R$ is not the correct explanation of $A$.

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(B) In $S.H.M$,the kinetic energy $(K.E)$ and potential energy $(P.E)$ are given by:$K.E = \frac{1}{2} m \omega^2 (a^2 - y^2)$$P.E = \frac{1}{2} m \omega^2 y^2$where $a$ is the amplitude and $y$ is the displacement.For $K.E = P.E$:$\frac{1}{2} m \omega^2 (a^2 - y^2) = \frac{1}{2} m \omega^2 y^2$$a^2 - y^2 = y^2$$a^2 = 2y^2$$y = \pm \frac{a}{\sqrt{2}}$Thus,Assertion $(A)$ is true.Regarding Reason $(R)$,the potential energy of a particle in $S.H.M$ is indeed periodic and reaches its maximum value at the extreme displacement $(y = \pm a)$. However,this statement does not explain why the kinetic and potential energies are equal at $y = a/\sqrt{2}$. Therefore,both are true,but $(R)$ is not the correct explanation of $(A)$.

Assertion $(A)$: In $S.H.M$,kinetic and potential energy become equal when the distance is $1/\sqrt{2}$ times its amplitude. Reason $(R)$: The potential energy of a particle executing $S.H.M$ is periodic with time period being maximum at the extreme displacement.

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