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Question
Compute the time period for the following system if the block of mass m is slightly displaced vertically down from its equilibrium position and then released. Assume that the pulley is light and smooth, strings and springs are light.
Solution
Case (a): Pulley is fixed rigidly here. When the mass displace by y and the spring will also stretch by y.
Therefore, F = T = ky
T = `2π sqrt("m"/"k")`
Case (b): Mass displace by y, pulley also displaces by y.
T = 4ky
T = `2π sqrt("m"/(4"k"))`
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