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 \(\varphi\) and \(\xi\) 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 \(\varepsilon\) 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.

在本文中，钟摆模型由一个机械系统表示，该系统由悬挂在弹簧上的简单钟摆组成，允许在平面内振荡。悬挂点在半径 (a) 的圆形路径中移动，该路径足够大。有两个自由度来描述命名的运动；摆的角位移和弹簧的伸长量。使用拉格朗日方程获得广义坐标\(\varphi\)和\(\xi\)方面的运动方程。这些方程的近似解在一个大参数\(\varepsilon\)将被定义而不是以前研究中的小。使用计算机程序获得系统参数对运动的影响。获得的计算机研究通过图形表示显示了所用方法的准确性。