Question

A particle is executing S.H.M between two points P and Q with zero velocity at these two points which are the distances ‘a’ and ‘b’ from a fixed point ‘O’ in the same line OPQ. The velocity of particle midway between the points P and Q is V. The time period of oscillation of the particle is

• A. $\frac{\pi (a+b)}{V}$
• B. $\frac{\pi (b-a)}{V}$
• C. $\frac{\pi (a+b)}{2V}$
• D. $\frac{\pi (b-a)}{2V}$

Answer 1

The correct option is B $\frac{\pi (b-a)}{V}$

$Amplitude\left(A\right)=\left(\frac{b-a}{2}\right);V_{max}=A\omega$
$V=\left(\frac{b-a}{2}\right)\times \frac{2\pi }{T}T=\frac{\pi (b-a)}{V}$