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Two particles are executing SHM and have the same time period. If at the same time one particle is at one extreme point and other is at another extreme point, find the phase difference between them.

Two particles are executing SHM and have the same time period. If at the same time one particle is at one extreme point and other is at another extreme point, find the phase difference between them. Correct Answer 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.

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