A spring of force constant 200 N m - 1 has a block of mass 10 kg hanging at its one end and the other end of the spring is attached to the ceiling of an elevator. The elevator is rising upwards with an acceleration of g 4 and the block is in equilibrium with respect to the elevator. When the acceleration of the elevator suddenly ceases, the block starts oscillating. What is the amplitude (in m ) of these oscillations?

Question

A spring of force constant 200 N m - 1 has a block of mass 10 kg hanging at its one end and the other end of the spring is attached to the ceiling of an elevator. The elevator is rising upwards with an acceleration of g 4 and the block is in equilibrium with respect to the elevator. When the acceleration of the elevator suddenly ceases, the block starts oscillating. What is the amplitude (in m ) of these oscillations?,

MARKS App · Accepted Answer

When elevator is moving up, using NLM, T − mg = mg 4 ⇒ T = 5 mg 4 This tension elongates the spring by x, T = kx ⇒ x = 5 mg 4 k The equilibrium position of the block is, x 0 = mg k So the amplitude is, A = x − x 0 = 5 mg 4 k − mg k = mg 4 = 0 .125 m

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