Correct Answer - Option 3 : 180°
CONCEPT:
-
Simple harmonic motion occurs when the restoring force is directly proportional to the displacement from equilibrium.
⇒ F α -x
Where F = force and x = the displacement from mean position or equilibrium.
- The equation of displacement in Simple Harmonic Motion is given by:
⇒ x = A sin(ωt + ϕ)
where the amplitude is A, ω is the angular frequency (ω = 2π/T), ϕ is the initial phase, and x is the distance from the mean position with respect to time t.
CALCULATION:
- Let the equation of displacement of SHM is
⇒ x = A sin(ωt + ϕ)
- Given that at the same time one particle is at one extreme point and other is at another extreme point,
- At one extreme point displacement x = A. So equation will be
⇒ A = A sin(ωt + ϕ)
⇒ sin(ωt + ϕ) = 1
⇒ ωt + ϕ = 90°
- At the other extreme point displacement x = - A. So equation will be
⇒ -A = A sin(ωt + ϕ)
⇒ sin(ωt + ϕ) = - 1
⇒ ωt + ϕ = 270°
- So the phase difference between them will be
⇒ Δϕ = 270° - 90° = 180° or π
- Hence the correct answer is option 3.