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A body moves along a straight line $O A B$ simple harmonically. It has zero velocity at the points $A$ and $B$ which are at distances $a$ and $b$ respectively from $O$ and has velocity $v$ when half way between them. Find the period of $S H M$ .

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$\frac{π (b + a)}{v}$

$\frac{π (b - a)}{v}$

$\frac{b - a}{πv}$

$\frac{2 (b - a)}{v}$

answer is A.

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Detailed Solution

It is clear from the figure that $C$ is the mean position of $S H M$ . The amplitude of oscillation

$A = \frac{b - a}{2}$

The velocity of mean position will be

$v = ω A = \frac{2 π}{T} (\frac{b - a}{2}) T = \frac{π (b - a)}{v}$

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