A case of plane rotations of an elastic pendulum

The motion of a point mass, suspended on a spring in a uniform gravity field, is investigated. The spring is assumed to be weightless and to possess linear elasticity. Motion occurs in a specified fixed vertical plane. It is shown that a pendulum motion exists in which the angle, made by the axis of the spring and the vertical, varies uniformly with time. The problem of the orbital stability of this motion is solved.