Elastic Potential Energy
Recall that Hooke's law for springs states that there is a restoring force given by where x is measured from equilibrium position of the spring. Let's use this force to find an expression for the associated potential energy of a spring.
The place to start is always to calculate the work done by the conservative force - in this case using Hooke's law for springs. Once we have this result, we will flip its sign and call it the change in potential energy just as we saw in the second section of this chapter when potential energy was derived.
Elastic Potential Energy Derivation
The calculation goes like this: