Elastic potential energy is the energy stored as a result of the deformation of an elastic object, such as the stretching of a spring. An object is elastic if it returns to its original shape and size after being deformed.
Potential energy is also associated with the elastic force exerted by an ideal spring. The work done by this force can be represented as a change in the elastic potential energy of the spring. Thus, the work done by a perfectly elastic spring, in one dimension, depends only on the spring constant and the squares of the displacements from the unstretched position. This work only involves the properties of a Hooke’s law interaction, in which a restoring force is proportional to and in the opposite direction of the imposed displacement, and not the properties of real springs and whatever objects are attached to them. Therefore, the difference in elastic potential energy for a spring force can be defined as the negative of the work done by the spring force.
A simple system embodying both gravitational and elastic potential energy is a one-dimensional, vertical mass-spring system. This consists of a massive particle (or block) hung from one end of a perfectly elastic, massless spring, the other end of which is fixed.
This text is adapted from Openstax, University Physics Volume 1, Section 8.1: Potential Energy of a System.
