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## Homework Statement

Find the time period of the oscillations of the body whose mass is m when it is displaced slightly form equilibrium. All springs have spring constant k and the pulleys and strings are massless and frictionless.

## Homework Equations

[itex]T=2∏\sqrt{\frac{m}{K}}[/itex]

where T is the time period of oscillations

m is the mass of the body, K is the effective force constant.

## The Attempt at a Solution

I've tried to find the net displacement hoping that it would help.

When the body is pulled by a distance x from equilibrium, the spring 1 extends by x. Then this force due to extension on the pulley must be balanced by the tension and extension of spring 2. Since the latter two are equal, spring 2 must extend by 0.5x. Similarly, spring 3 must extend by 0.25x.

So the next displacement of the block is [itex]\frac{7x}{4}[/itex].

I don't know what to do after that to find the effective force constant on the block.