A new pendulum motion with a suspended point near infinity
Abstract 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 o...
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Nature Portfolio
2021
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oai:doaj.org-article:7eac42022c0643aba541d224b9f2038f2021-12-02T17:12:18ZA new pendulum motion with a suspended point near infinity10.1038/s41598-021-92646-62045-2322https://doaj.org/article/7eac42022c0643aba541d224b9f2038f2021-06-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-92646-6https://doaj.org/toc/2045-2322Abstract 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 $$\varphi$$ φ and $$\xi$$ 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 $$\varepsilon$$ 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.A. I. IsmailNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-7 (2021) |
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Medicine R Science Q |
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Medicine R Science Q A. I. Ismail A new pendulum motion with a suspended point near infinity |
| description |
Abstract 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 $$\varphi$$ φ and $$\xi$$ 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 $$\varepsilon$$ 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. |
| format |
article |
| author |
A. I. Ismail |
| author_facet |
A. I. Ismail |
| author_sort |
A. I. Ismail |
| title |
A new pendulum motion with a suspended point near infinity |
| title_short |
A new pendulum motion with a suspended point near infinity |
| title_full |
A new pendulum motion with a suspended point near infinity |
| title_fullStr |
A new pendulum motion with a suspended point near infinity |
| title_full_unstemmed |
A new pendulum motion with a suspended point near infinity |
| title_sort |
new pendulum motion with a suspended point near infinity |
| publisher |
Nature Portfolio |
| publishDate |
2021 |
| url |
https://doaj.org/article/7eac42022c0643aba541d224b9f2038f |
| work_keys_str_mv |
AT aiismail anewpendulummotionwithasuspendedpointnearinfinity AT aiismail newpendulummotionwithasuspendedpointnearinfinity |
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1718381442223833088 |