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(A) In $SHM$,the total mechanical energy $E$ is the sum of kinetic energy $K.E.$ and potential energy $P.E.$.$E = K.E. + P.E. = \frac{1}{2} m v^2 + \f

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Always constant

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(A) In $SHM$,the total mechanical energy $E$ is the sum of kinetic energy $K.E.$ and potential energy $P.E.$.$E = K.E. + P.E. = \frac{1}{2} m v^2 + \frac{1}{2} k x^2$.Substituting $x = A \sin(\omega t + \phi)$ and $v = A \omega \cos(\omega t + \phi)$,we get $E = \frac{1}{2} m A^2 \omega^2 \cos^2(\omega t + \phi) + \frac{1}{2} k A^2 \sin^2(\omega t + \phi)$.Since $k = m \omega^2$,the expression simplifies to $E = \frac{1}{2} k A^2 (\cos^2(\omega t + \phi) + \sin^2(\omega t + \phi))$.Using the identity $\sin^2 	heta + \cos^2 	heta = 1$,we get $E = \frac{1}{2} k A^2$.Since $k$ (force constant) and $A$ (amplitude) are constants,the total mechanical energy remains constant throughout the motion.

The total mechanical energy of a particle in $SHM$ is

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