The extension produced x is directly proportional to the force applied to extend or compress the spring. F=kx were k is spring constant. The work done to stretch or compress the spring is stored as its PE W= integral 0 to x (Fdx) =0 to x (kxdx) =1/2 kx^2
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The characteristic of a spring is that the force needed to stretch or compress a spring by an amount x is equal to k x and is in the direction opposite to the extension or compression. Here k is called the spring constant.
     Restoration Force of the spring (compression or tensile) Fs = - k x  = - external force F
     Work done by the external force in compressing the spring from x = 0 to x = L can be obtained by:

W =  \int\limits^L_0 {F .} \, ds =  \int\limits^L_0 {( k x)} \, dx,\ \ \ \ as\ displacement\ s= x\\ \\ W =  k\int\limits^L_0 {x} \, dx = \frac{1}{2}k [x^2 ]_0^L = \frac{1}{2}k\ L^2 =\frac{1}{2}k x^2\\  is the energy given by the external force to the spring with an extension x. 

This energy is stored as potential energy in the spring.

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