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Two identical springs of spring constant...

Two identical springs of spring constant k are attached to a block of mass m and to fixed supports as shown in figure. When the mass is displaced from equilibrium position by a distance x towards right, find the restoring force.

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According to below figure block is displaced to right side at distance x.

The right spring gets compressed by x developing a restoring force kx towards left on the block. The left spring is stretched by an amount x developing a restoring force kx left on the block F.B.D. for this is as below.

Hence, total restoring force towards left on the block,
`F= kx +kx`
`therefore F= 2kx`.
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