A Spring-Mass System. A mass m supported by a frictionle

A Spring-Mass System. A mass m supported by a frictionless horizontal surface is attached to a spring that is, in turn, attached to a fixed support. Assuming that motion is restricted to one direction, let x(t) represent the displacement of the mass from its equilibrium position. This position corresponds to the spring being at its rest length. If the spring is compressed, then x < 0 and the mass is left of its equilibrium position. If the spring is elongated, then x > 0 and the mass is right of its equilibrium position. Assume that the potential energy stored in the spring is given by kx2?2, where the parameter k is the spring constant of the spring. Find the action integral and Euler