Question

Two particles P and Q start from the origin and execute simple harmonic motion along x – axis with the same amplitude and time periods 3 s and 6 s respectively. The ratio of the velocities of P and Q when they meet is

• A. 1:2
• B. 2:1
• C. 2:3
• D. 3:2

Answer 1

The correct option is B 2:1

$x_1=Asin\left(w_{1}t\right)$ , $w_1=\frac{2\pi }{3},w_2=\frac{2\pi }{6}$
$x_2=Asin\left(w_{2}t\right)$
when the particles meet each other their positions are equal
$x_1=x_2\to sin\left(w_{1}t\right)=sin\left(w_{2}t\right)$
$\to w_{1}t=\pi -w_{2}t$
$\to (w_1+w_2)t=\pi \to t=1s$
$v_1=A{w}_{1}cos\left(w_{1}t\right)$ , $v_2=A{w}_{2}cos\left(w_{2}t\right)$
$\therefore \frac{v_1}{v_2}=\frac{w_1}{w_2}\times \frac{cos\left(\frac{2\pi }{3}\right)}{cos\left(\frac{\pi }{3}\right)}=\frac{2}{1}$