Hooke's law is a law which states that the force, F, required to bend a spring (or some other elastic object) is directly proportional to the distance X by some constant k, known as the stiffness constant. This is sometimes written as In this case, F is equal to the force with which the spring pushes back. By integrating with respect to x, we can find the work needed to compress or stretch a spring a given distance and the potential energy stored in said spring.