For an object obeying Hooke's Law, the potential energy is given by
where Dx is the displacement from the equilibrium point.
Example:
A 20kg mass is suspended from a spring that is hanging from a support. When the mass is at rest, it hangs .15m below the support. Now assume the spring-mass system is placed on a horizontal frictionless surface. What is the potential energy of the mass when it is a distance .1m from the support?
To be able to use equation (13), it is necessary to find k. When the mass is hanging at rest, it is at its equilibrium point. The forces acting on the mass are gravity, pulling down on the mass, and the force of the spring, supporting the mass. Since the spring is at rest, the acceleration is 0, and the forces must be equal in magnitude.
