Question

Two particles A and B perform SHM along the straight line with the same amplitude ${}^{\prime }{a}^{\prime }$, same frequency ${}^{\prime }{f}^{\prime }$ and same equilibrium position ${}^{\prime }{O}^{\prime }$. The greatest distance between them is found to be $\frac{3a}{2}$. At some instant of time, they have the same displacement from mean position. What is the displacement?

Answer 1

Let the chosen instant $p$ makes an angle $\theta$ with x-axis then.

$cos\theta =\frac{3\frac{A}{4}}{A}=\frac{3}{4}\Rightarrow sin\theta =\frac{\sqrt{7}}{4}$

The phase differences between two particles

$cos(\frac{\pi }{2}-\theta )=\frac{x}{A}\Rightarrow x=Acos(\frac{\pi }{2}-\theta )Asin\theta =\frac{A\sqrt{7}}{4}$

Displacement$=\frac{A\sqrt{7}}{4}$