Question
Two identical springs of spring constant K are attached to a block of mass m and to fixed supports as shown in Fig. When the mass is displaced from equilllibrium position by a distance x towards right, find the restoring force.
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Answer
When mass is displaced from equilibrium position by a distance x towards right, 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.
Developing a restoring force $K x$ towards Left on the block. $F_1=-K x$ (for left spring) and $F_2=-K x$ (for right spring) Restoring force, $\mathrm{F}=\mathrm{F}_1+\mathrm{F}_2=-2 \mathrm{Kx} .: \mathrm{F}=2 \mathrm{Kx}$ towards left.
Developing a restoring force $K x$ towards Left on the block. $F_1=-K x$ (for left spring) and $F_2=-K x$ (for right spring) Restoring force, $\mathrm{F}=\mathrm{F}_1+\mathrm{F}_2=-2 \mathrm{Kx} .: \mathrm{F}=2 \mathrm{Kx}$ towards left.
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