Consider an ideal spring, with spring constant k, which is oriented along an x-axis. one end of the spring is fixed, and the free end is located at x = 0 when the spring is neither stretched nor compressed. an object having a mass m is attached to the free end of the spring. consider an action in which the free end of the spring is moved from an initial position xi to a final position xf. the work done by the spring (and on the object attached to the free end) during this action is given by