Q. Two particles executes S.H.M. of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions, and each time their displacement is half of their amplitude. The phase difference between them is
A) $30{^\circ}$
B) $60{^\circ}$
C) $90{^\circ}$
D) $120{^\circ}$
Explanation
(d) $y = a\sin{(\omega t + \phi_{0})}.$ According to the equation
$y = \frac{a}{2} \Rightarrow \frac{a}{2} = a\sin{(\omega t + \phi_{0})} \Rightarrow \left( \omega t + \phi_{0} \right) = \phi = \frac{\pi}{6}\ or\ \frac{5\pi}{6}$
Physical meaning of $\phi = \frac{\pi}{6}\ :\ $Particle is at point $P$ and it is going towards $B$
Physical meaning of $\phi = \frac{5\pi}{6}\ :$ Particle is at point $P$ and it is going towards $O$
So phase difference $\Delta\phi = \frac{5\pi}{6} - \frac{\pi}{6} = \frac{2\pi}{3} = 120{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.