A new pendulum motion with a suspended point near infinity

In this paper, a pendulum model is represented by a mechanical system that consists of a simple pendulum suspended on a spring, which is permitted oscillations in a plane. The point of suspension moves in a circular path of the radius (a) which is sufficiently large. There are two degrees of freedom for describing the motion named; the angular displacement of the pendulum and the extension of the spring. The equations of motion in terms of the generalized coordinates [Formula: see text] and [Formula: see text] are obtained using Lagrange's equation. The approximated solutions of these equations are achieved up to the third order of approximation in terms of a large parameter [Formula: see text] will be defined instead of a small one in previous studies. The influences of parameters of the system on the motion are obtained using a computerized program. The computerized studies obtained show the accuracy of the used methods through graphical representations.