Q: A particle performs SHM with a period T and amplitude *a*. The mean velocity of the particle over the time interval during which it travels a distance *a*/2 from the extreme position is

(a) *a*/T

(b) 2*a*/T

(c) 3*a*/T

(d) *a*/2T

Ans: (c)

Sol: $\large y = a cos\omega t $

$\large a/2 = a cos\omega t $

$\large 1/2 = cos\omega t $

$\large cos\pi/3 = cos\omega t $

$\large t = \frac{\pi}{3\omega} = \frac{T}{6}$

Mean velocity $\large v_m = \frac{a/2}{T/6} = \frac{3a}{T}$