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Two identical springs (spring constant = k ) are connected to two light rigid rods in parallel combination and then a third spring (identical to the other two) is connected to this combination in series. The combined system is fixed to the ceiling and a block of mass m is attached as shown in the figure. If the mass is slightly displaced and then let go, then the system shall oscillate with a time period of

Options

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

Correct answer

B. 2 π 3 m 2 k

Step-by-step solution

Consider the system as shown in figure below. Here, k 2 and k 3 are in parallel. k 1 is in series with parallel combination of k 2 and k 3 . Effective spring constant of the combination is k e f f = k 2 + k 3 k 1 k 1 + k 2 + k 3 = 2 k × k 3 k = 2 3 k ∴ Time period of oscillation T = 2 π m k e f f = 2 π m 2 3 k = 2 π 3 m 2 k

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