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

A particle of mass m is connected to three springs A , B , and C having equal force constants k , as shown in the figure. If the particle is pushed slightly against spring C and then released, determine its time period of oscillation.

Options

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

Correct answer

B. 2 m 2k

Step-by-step solution

Let the mass be at the origin (0,0) . The directions of the springs are: Spring A: along the positive x-axis ( i ) Spring B: along the positive y-axis ( j ) Spring C: at 45^ to the negative x-axis, along - 1 2 i - 1 2 j When the particle is displaced by a small distance x against spring C, the displacement vector is: s = x (- 1 2 i - 1 2 j ) The extensions (or compressions) in the springs are the components of s along their respective directions: For spring C, the displacement is directly along its axis, so it is c

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