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(D) In Simple Harmonic Motion $(S.H.M.)$,the displacement $x$ is given by $x = A \sin(\omega t + \phi)$.The velocity $v$ is the derivative of displace

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(D) In Simple Harmonic Motion $(S.H.M.)$,the displacement $x$ is given by $x = A \sin(\omega t + \phi)$.The velocity $v$ is the derivative of displacement with respect to time: $v = \frac{dx}{dt} = A\omega \cos(\omega t + \phi)$.At the mean position,the displacement $x = 0$,which implies $\sin(\omega t + \phi) = 0$,so $\cos(\omega t + \phi) = \pm 1$.Therefore,the magnitude of velocity is $|v| = A\omega$,which is the maximum possible value for the velocity in $S.H.M.$

The velocity of a particle performing simple harmonic motion,when it passes through its mean position is

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