Potential energy is tile energy associated with
the relative positions of two or more interacting
particles. Potential energy fits well the idea of
energy as the capacity to do work. For example,
the gravitational potential energy of an object
raised off the ground can be used to compress
or expand a spring or to lift another weight. As
a coil spring unwinds, or a straight spring
returns to its natural length, the stored
potential energy can be used to do work. For
example, if a block is attached to a compressed
spring, the elastic potential


The work done by the spring force When the displacement of the free end changes from `x_i` to
`x_f` is given by equation.

`W_s=1/2k(x_f^2-x_i^2)`

By definition `W_s =-Delta U_s=-(U_f-U_i)`

therefore, `U_f=U_i+1/2k(x_f^2-x_i^2)`

`U_s=1/2 kx^2`..................(2)

If we assume the potential energy stored in the spring at equilibrium `X` is zero and all the displacements are measured from equilibrium,
then `x_i= 0` and `U_i= 0` .

Thus, final energy stored in the spring is `(U_f = 1/2 kx^2)`

The potential energy function for an ideal spring is a parabolic function as in fig .