Question

obtain an expression for potential energy of a spring

Answer 1

Elastic potential energy is Potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched. According to Hooke's law, the force required to stretch the spring will be directly proportional to the amount of stretch.

Since the force has the form

F = -kx

then the work done to stretch the spring a distance x is

Work = Triangle PE = 1/2kx X 1/2kx