Question

Two particles execute SHM of the same amplitude and frequency along the same line. They pass one another when going in opposite directions each time their displacement is half their amplitude. Show that the phase difference between them is 120°.

Answer 1

Let the equations be

Let the particles cross each other at t = 0, so that

At t = 0, x₁ = Aω cos ϕ₁ = + ve and x₂ = Aω cos ϕ₂ = – ve 

which show that the particles are moving in opposite directions. 

Phase difference = ϕ ₂ – ϕ ₁ = 120°.