Whenever a system interacts with its surroundings, it can exchange  energy  in  two  ways- work and heat.

In mechanics, work is defined as the product of the force and the displacement  in  the  direction of the force.


Work done when a spring is compressed or extended: According to Hooke's law


Spring force = - k (x – x0)


Where k is the spring constant, x0 is the equilibrium position, and x is the final position. The negative sign shows that the direction of the spring force is opposite the direction of the displacement from x0. The external force is equal in magnitude but opposite in sign to the  spring force, so


External force (force of your hands) = k (x –x0).


Now, we want to calculate the work done when we stretch the spring from position 1  to position 2.


                        W = F dx = k (x – x0) d(x-x0) = 1/2 k [(x2-x0)2 - (x1-x0)2]
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