Question

Two particles execute SHM of same amplitude and same time period, about same mean position but with a phase difference between them. At an instant they are found to cross each other at $x=+\frac{A}{3}$. The phase difference between them is:

• A. $2co{s}^{-1}\left[\frac{1}{5}\right]$
• B. $2si{n}^{-1}\left[\frac{1}{5}\right]$
• C. $2co{s}^{-1}\left[\frac{1}{3}\right]$
• D. $2si{n}^{-1}\left[\frac{1}{3}\right]$

Answer 1

The correct option is C $2co{s}^{-1}\left[\frac{1}{3}\right]$

Clearly,
$Acos\theta =\frac{A}{3}$
$\Rightarrow \theta =co{s}^{-1}\left[\frac{1}{3}\right]$
$\therefore Phasedifference,△\varphi ={\varphi }_2-{\varphi }_1$
$\Rightarrow 2\theta =2co{s}^{-1}\left[\frac{1}{3}\right]$