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Find the time period of mass M when displaced from its equilibrium position and then released for the system shown in the figure.

Answer:

y represents the distance across which the mass is pulled.

The spring’s total extension is y + y = 2y.

The initial mean location of equilibrium = x0

In the spring, the net extension is equal to x0 + 2y.

When the equation F = 2T is solved with T = kx0, the result is

We obtain a being proportionate to –x

When we compare the above acceleration to the usual SHM equation, we get

2 = 4k/m

ꞷ = √4k/M