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Manipal MET2013PhysicsOscillations

The angular velocities of three bodies in simple harmonic motion are ₁, ₂, ₃ with their respective amplitudes as A₁, A₂, A₃ If all the three bodies have same mass and velocity, then

Options

  1. AA₁^2 ₁^2=A₂^2 ₂^2=A₃^2 ^2
  2. BA₁^2 ₁=A₂^2 ₂=A₃^2 ₃
  3. CA₁ ₁^2=A₂ ₂^2, A₃ ₃^2
  4. DA₁ ₁=A₂ ₂=A₃ ₃

Correct answer

D. A₁ ₁=A₂ ₂=A₃ ₃

Step-by-step solution

Rate of change of displacement is known as velocity. The equation for displacment ( y ) of a body in SHM with angular velocity is given by y=a t where a is amplitude velocity v= rate of change of displacement = d y d t v= d y d t = d d t (a t)=a t Given, v₁=v₂=v₃ and a₁=A₁, a₂=A₂ . a₃=A₃A₁ ₁=A₂ ₂=A₃ ₃

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