Question

Time period $(T)$ and amplitude $(A)$ are same for two particles which undergo SHM along the same line. At one particular instant, one particle is at phase $\frac{3 \pi}{2}$ and other is at phase zero. While moving in the same direction. Find the time at which they will cross each other.

• A. 4T/2
• B. 3T/8
• C. 3T/4
• D. 3T/7

Answer 1

Answer: (B)

At phase $3 \pi / 2,(\omega t+\phi)=3 \pi / 2$
$x_{1}=A \sin \frac{3 \pi}{2}=-A$
$x_{2}=0$
So, at $t=0, x_{1}=-A \cos \omega t$ and $x_{2}=A \sin \omega t$
$x_{1}=x_{2}$
$-\cos \omega t=\sin \omega t$
$\tan \omega t=-1$
$\omega t=\frac{3 \pi}{4}$
$\left(\frac{2 \pi}{T}\right) t=\frac{3 \pi}{4}$
$t=3 T / 8$