ELASTIC POTENTIAL ENERGY

One end of an elastic spring of negligible mass
and obeying Hooke’s law is tied with a rigid wall

and to the other end a block of mass m is tied.

The block is at x = 0 when the spring is not
extended or compressed. On displacing the block,
the restoring force is produced in the spring
which tries to restore the block to its original
position.

The restoring force is directly proportional to the
displacement of the block and is in a direction opposite to the displacement.
∴ F ∝ - x or F = - kx, where k is the force constant of the spring which is defined as the force required to pull or compress the spring by unit displacement. Its unit is N /m and its dimensional formula is M1 L0 T -2.

This work done on the spring is stored in the form of elastic potential energy of the spring. Taking the potential energy to be zero for x = 0, for change in length equal to x, the potential stored in the spring will be
U = 1 / 2 kx2