Question

Two particles $P$ and $Q$ describe SHM of same amplitude $a$ and frequency $f$ along the same straight line. The maximum distance between two particles is $a\sqrt{2}$. The initial phase difference between the particles is:

• A. $\text{Zero}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is A $\text{Zero}$

let the phase difference = z

the equation of displacement of the particle p from origin

$y=rsin(\omega t+z)$

the equation of displacement of the particle q from origin

$x=rn\left(\omega t\right)$

$2rsin\left(\frac{z}{2}\right)=\frac{r}{\sqrt{2}}$

given max distance between the particles is $\sqrt{2}r$

hence maximum phase difference is zero