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A mass m on the end of an ideal spring stretches the spring to a length when at rest. The mass is now set into motion so that it executes up and down vibrations while swinging back and forth as a simple pendulum. The mass moves in a figure eight pattern in a vertical plane a shown in the figure. The force constant of the spring assuming small oscillations is

Options

  1. Amg
  2. B2 mg k
  3. C4 mg
  4. Dmg 2

Correct answer

C. 4 mg

Step-by-step solution

For vertical oscillation time period T ₁=2 m k /ldots(i) For the transverse oscillation period of simple pendulum T₂=2 g But 2 ~T ₁= T ₂ k = 4 mg

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