Q. A system shown in the figure consists of a massless pulley, a spring of force constant and a block of mass . If the block is slightly displaced vertically downwards from its equilibrium position and released, then the period of vertical oscillations is

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Solution:

In this situation, if mass m moves downwards a distance from the equilibrium position, the pulley will also move by x and so, the spring will stretch by .
Therefore, the spring force will be . The restoring force on the block will be .
Hence,

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