Work Done by a Massless Linear Spring Force

The force required to stretch an ideal spring is given by

where k is the spring modulus, and l, l_o, and delta are the present length, unstretched length, and deformation of the spring from its unloaded position, respectively.

Since the force exerted on the particle is not constant, the work done on the particle must be computed using integration.

When a particle that is attached to an elastic spring moves to increase the stretch in the spring, the spring will do negative work on the particle.