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

As shown in the figure, a spring with constant k = 100 N/m is attached to a block of mass M = 1 kg . A constant force F = 10 N acts on the block. While the block is in its equilibrium position, a sharp blow by an external agent imparts a speed of 2 m/s to the block towards the left. Which of the following statements are correct?

Options

  1. AThe time period of the resulting simple harmonic motion is 5 s .
  2. BThe amplitude of the resulting simple harmonic motion is 20 cm .
  3. CThe potential energy of the spring when the block is at the right extreme is 2.5 J .
  4. DThe potential energy of the spring when the block is at the left extreme is 4.5 J .

Correct answer

D. The potential energy of the spring when the block is at the left extreme is 4.5 J .

Step-by-step solution

At the equilibrium position, the spring force balances the constant external force F . Let the compression in the spring be x₀ . k x₀ = F 100 x₀ = 10 x₀ = 0.1 m = 10 cm The angular frequency of the SHM is = k M = 100 1 = 10 rad/s . The time period is T = 2 = 2 10 = 5 s . Since the blow is given at the equilibrium position, the imparted speed is the maximum velocity of the SHM. v_ max = A 2 = A 10 A = 0.2 m = 20 cm The block oscillates about the equilibrium position ( 10 cm compression) with an amplitude of 20 cm .

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