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Concepts Of Physics MCQ Edition [Volume 1]PhysicsSimple Harmonic Motion

Three springs A , B , and C , each having a force constant k , are attached to a particle of mass m . Initially, the angle between any two springs is 120^ . If the particle is slightly pushed against spring C and then released, determine its time period of oscillation.

Options

  1. A2 2m 3k
  2. B2 m k
  3. C2 3m 2k
  4. D2 m 3k

Correct answer

A. 2 2m 3k

Step-by-step solution

Let the displacement of the particle be x towards spring C . The compression in spring C is x . The restoring force exerted by spring C is F_C = kx , directed opposite to the displacement. The angle between the line of action of spring C and those of springs A and B is 120^ . The extension in springs A and B is the component of displacement along their respective lengths, which is x (180^ - 120^ ) = x 60^ = x 2 . The restoring force exerted by each of springs A and B is F_A = F_B = k ( x 2 ) , directed towards thei

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