A S.H.M. has amplitude a and time period T. T | vedclass

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(D) The displacement of a particle in $S.H.M.$ is given by $x = a \sin(\omega t + \phi)$.Taking the derivative with respect to time,the velocity is $v

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$\frac{2\pi a}{T}$

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(D) The displacement of a particle in $S.H.M.$ is given by $x = a \sin(\omega t + \phi)$.Taking the derivative with respect to time,the velocity is $v = \frac{dx}{dt} = a\omega \cos(\omega t + \phi)$.The maximum velocity occurs when $\cos(\omega t + \phi) = 1$,so $v_{\max} = a\omega$.Since the angular frequency $\omega = \frac{2\pi}{T}$,substituting this into the expression gives $v_{\max} = a \left(\frac{2\pi}{T}\right) = \frac{2\pi a}{T}$.

$A$ $S.H.M.$ has amplitude $a$ and time period $T$. The maximum velocity will be

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