A particle performs SHM with a period T and a | vedclass

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(C) The equation for the displacement of a particle in $SHM$ starting from the extreme position is $x = a \cos(\omega t).$To travel a distance of $a/2

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$3a/T$

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(C) The equation for the displacement of a particle in $SHM$ starting from the extreme position is $x = a \cos(\omega t).$To travel a distance of $a/2$ from the extreme position $(x = a)$,the particle reaches the position $x = a - a/2 = a/2.$Substituting this into the equation: $a/2 = a \cos(\omega t) \Rightarrow \cos(\omega t) = 1/2.$Since $\cos(\pi/3) = 1/2,$ we have $\omega t = \pi/3.$Substituting $\omega = 2\pi/T,$ we get $(2\pi/T)t = \pi/3 \Rightarrow t = T/6.$The mean velocity is defined as the total displacement divided by the total time interval: $v_{av} = \frac{	ext{displacement}}{	ext{time}} = \frac{a/2}{T/6} = \frac{3a}{T}.$

$A$ 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

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