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(B) The displacement of the particles is given by $x_P = A \sin(\omega_P t)$ and $x_Q = A \sin(\omega_Q t)$.Given periods are $T_P = 3 \ s$ and $T_Q =

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(B) The displacement of the particles is given by $x_P = A \sin(\omega_P t)$ and $x_Q = A \sin(\omega_Q t)$.Given periods are $T_P = 3 \ s$ and $T_Q = 6 \ s$. Thus,angular frequencies are $\omega_P = \frac{2\pi}{3}$ and $\omega_Q = \frac{2\pi}{6} = \frac{\pi}{3}$.The particles meet when $x_P = x_Q$,which occurs at the mean position $(x=0)$ when $P$ completes one full oscillation and $Q$ completes half an oscillation.At the mean position,the velocity of a particle in Simple Harmonic Motion is maximum,given by $v = A\omega$.Therefore,the ratio of velocities is $\frac{v_P}{v_Q} = \frac{A\omega_P}{A\omega_Q} = \frac{\omega_P}{\omega_Q} = \frac{2\pi/3}{\pi/3} = \frac{2}{1}$.

Two particles $P$ and $Q$ start from the origin and execute Simple Harmonic Motion along the $X$-axis with the same amplitude but with periods $3 \ s$ and $6 \ s$ respectively. The ratio of the velocities of $P$ and $Q$ when they meet is

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