1. Tardigrade
  2. Question
  3. Physics
  4. Two particles undergoes SHM along parallel lines with the same time period (T) and equal amplitudes. At a particular instant, one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Two particles undergoes SHM along parallel lines with the same time period $(T)$ and equal amplitudes. At a particular instant, one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time.Physics Question Image

Oscillations

Solution:

This problem is easy to solve with the help of phasor diagram. First we draw the initial position of both the particle on the phasor as shown in figure.image
From above figure phase difference between both the particles is $\pi / 2$.They will cross each other when their projection from the circle on the horizontal diameter meet at one point. Let after time $t$ both will reach at $P' Q'$ point having phase difference $\pi / 2$ as shown in figure.
image
Both will meet at $-A / \sqrt{2}$
When they meet angular displacement of $P$ is
$\theta=\frac{\pi}{2}+\frac{\pi}{4}=\frac{3 \pi}{4}$
So they will meet after time $t=\frac{3 \pi}{4 \times \omega}$
$t=\frac{3 \pi}{4 \times 2 \pi} \times T=\frac{3 T}{8} sec$