Two particles $P$ and $Q$ start from origin and execute simple harmonic motion along $X$-axis with the same…
Two particles $P$ and $Q$ start from origin and execute simple harmonic motion along $X$-axis with the same amplitude but with period $3 \mathrm{~s}$ and $6 \mathrm{~s}$, respectively. The ratio of the velocities of $P$ and $Q$ when they meet is
$1: 2$
$2: 1$
$2: 3$
$3: 2$
Solution
Ratio of velocities
$\begin{aligned} & \frac{v_1}{v_2}=\frac{A \omega_1}{A \omega_2}=\frac{\omega_1}{\omega_2} \\ = & \frac{2 \pi}{\frac{T_1}{2 \pi}}=\frac{T_2}{T_2} \Rightarrow=\frac{6}{3}\end{aligned}$
$v_1: v_2=2: 1$