Question

Two particles $P_1$ and $P_2$ are performing SHM along the same line about the same mean position. Initially, they are at their positive extreme position. If the time period of each particle is 12 s and the difference of their amplitudes is 12 cm then find the minimum time (in seconds) after which the separation between the particles become 6 cm.

Answer 1

Answer: 2

The $\text{x}$ coordinates of the particles are
$x_1=A_{1}cos\omega t,x_2=A_{2}cos\omega t$
Separation $x_1-x_2=\left(A_1-A_2\right)cos\omega t=12cos\omega t$
Now $x_1-x_2=6=12cos\omega t$
$\Rightarrow \omega t=\frac{\pi }{3}\Rightarrow \frac{2\pi }{12}\times t=\frac{\pi }{3}$
$\Rightarrow t=2s$