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


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

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