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(D) In an undamped simple harmonic motion $(S.H.M.)$,the total mechanical energy is given by $E = \frac{1}{2} k A^2$,where $k$ is the force constant a

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Infinite

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(D) In an undamped simple harmonic motion $(S.H.M.)$,the total mechanical energy is given by $E = \frac{1}{2} k A^2$,where $k$ is the force constant and $A$ is the amplitude.Since $k$ and $A$ are constants for a given $S.H.M.$,the total mechanical energy $E$ remains constant with respect to time.$A$ constant value does not oscillate,meaning its frequency of oscillation is $0$.Since the time period $T'$ is the reciprocal of frequency $(T' = 1/f)$,for $f = 0$,the time period $T'$ is infinite.Therefore,the correct option is $D$.

If a particle is executing simple harmonic motion with time period $T$,then the time period of its total mechanical energy is ...........

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