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JEE Main202225 Jul 2022Morning ShiftPhysicsOscillationsActual

In figure (A), mass 2 m is fixed on mass m which is attached to two springs of spring constant k . In figure (B), mass m is attached to two spring of spring constant k and 2 k . If mass m in (A) and (B) are displaced by distance x horizontally and then released, then time period T 1 and T 2 corresponding to (A) and (B) respectively follow the relation.

Options

  1. AT 1   T 2 = 3 2
  2. BT 1   T 2 = 3 2
  3. CT 1   T 2 = 2 3
  4. DT 1 T 2 = 2 3

Correct answer

A. T 1   T 2 = 3 2

Step-by-step solution

The time period of spring block system is given by T = 2 π m k . In both the cases springs are connected in parallel, In case 1 : k e q = 2 k and total mass is 3 m . Therefore, T 1 = 2 π 3 m k e q = 2 π 3 m 2 k In case 2 :   k e q = 3 k and total mass is m . Therefore, T 2 = 2 π m 3 k ⇒ T 1 T 2 = 9 2 = 3 2

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