Question

Two particles execute S.H.M. of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half the amplitude. The phase difference between them is ______.

(sin 30° = 0.5)

Options

• `pi/6`

• `(5 pi)/6`

• `pi/3`

• `(2 pi)/3`

Answer 1

Two particles execute S.H.M. of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half the amplitude. The phase difference between them is `bbunderline((2 pi)/3)`.

Explanation:

Let the displacements be:

x₁​ = A sin (ωt),

x₂​ = A sin (ωt + ϕ)

They meet at displacement x = `A/2`

sin (ωt) = `1/2`

⇒ ωt = `pi/6`

So,

x₂ = `A sin (pi/6 + Phi)`

Since they are in the same position:

`sin (pi/6 + Phi) = 1/2`

`pi/6 + Phi = `(5 pi)/6`

⇒ Φ = `(4 pi)/6`

= `(2 pi)/3`