Aforce of f stretches a certain spring a distance of x. what is the potential energy of the spring when a mass of m hangs vertically from it?

The elastic potential energy of a spring is:
 
where k is the spring constant and x is the displacement.

The spring constant k can be computed as the ratio between the force applied F and the displacement x:

But in our problem, the force that stretches the spring is the weight (mg) of the mass m that hangs from the spring, so:


Therefore, substituting k into the original formula, we can re-write the elastic potential energy as: