A new pendulum motion with a suspended point near infinity

• Published in: Scientific reports Vol. 11; no. 1; p. 13199
• Main Author: Ismail, A. I.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 24-06-2021; Nature Publishing Group; Nature Portfolio
• Subjects: 639/166/988; 639/705/1041; 639/766/25; Approximation; Humanities and Social Sciences; multidisciplinary; Oscillations; Science; Science (multidisciplinary)
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-021-92646-6

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
φ
and
ξ
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
ε
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.