Two particles $P$ and $Q$ start from origin and execute Simple Harmonic Motion along $X-$axis with same amplitude but with periods $3$ seconds and $6$ seconds respectively. The ratio of the velocities of $ P$ and $Q$ when they meet is
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(b) The particles will meet at the mean position when $P$ completes one oscillation and $Q$ completes half an oscillation
So $\frac{{{v_P}}}{{{v_Q}}} = \frac{{a{\omega _P}}}{{a{\omega _Q}}} = \frac{{{T_Q}}}{{{T_P}}} = \frac{6}{3} = \frac{2}{1}$
So $\frac{{{v_P}}}{{{v_Q}}} = \frac{{a{\omega _P}}}{{a{\omega _Q}}} = \frac{{{T_Q}}}{{{T_P}}} = \frac{6}{3} = \frac{2}{1}$
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