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I solved the problem applying a pseudo force mg on the block in the opposite direction to that of the elevator. I would appreciate highly if someone can solve without applying pseudo forces.

My solution:-As in the equilibrium position,the spring is stretched by mg/k,when we apply mg opposite to that of the weight,it instantly cancels the weight and only force left is kx and that makes it execute in S.H.M and mg/k is the extension when the block is at rest w.r.t. the elevator and so the amplitude.Please solve without pseudo force.Many thanks in advance.