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Multiple scales method for analyzing a forced damped rotational pendulum oscillator with gallows

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This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of rotational pendulum oscillators are studied and talked about in detail.These include the forced damped rotating pendulum oscillator with gallows,the damped standard simple pendulum oscillator,and the damped rotating pendulum oscillator without gallows.The MSM first-order approximations for all the cases mentioned are derived in detail.The obtained results are illustrated with concrete numerical examples.The first-order MSM approximations are compared to the fourth-order Runge-Kutta(RK4)numerical approximations.Additionally,the maximum error is estimated for the first-order approximations obtained through the MSM,compared to the numerical approximations obtained by the RK4 method.Furthermore,we conducted a comparative analysis of the outcomes obtained by the used method(MSM)and He-MSM to ascertain their respective levels of precision.The proposed method can be applied to analyze many strong nonlinear oscillatory equations.

rotational pendulum systemmultiple scales methodapproximate solutiondamped oscillationsforced pendulum with gallowshe-multiple scales method

Haifa A Alyousef、Alvaro H Salas、B M Alotaibi、S A El-Tantawy

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Department of Physics,College of Science,Princess Nourah bint Abdulrahman University,P.O.Box 84428,Riyadh 11671,Saudi Arabia

Department of Mathematics and Statistics,Universidad Nacional de Colombia,FIZMAKO Research Group,Colombia

Department of Physics,Faculty of Science,Port Said University,Port Said 42521,Egypt

Research Center for Physics(RCP),Department of Physics,Faculty of Science and Arts,Al-Mikhwah,Al-Baha University,Al-Baha 1988,Saudi Arabia

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Deanship of Scientific Research,Princess Nourah bint Abdulrahman UniversityProgram of Research Project Funding After Publication,grant No

44-PRFA-P-107

2024

10.1088/1572-9494/ad3192

理论物理通讯(英文版)
中国科学院理论物理研究所 中国物理学会

理论物理通讯(英文版)

CSTPCD
影响因子：0.333
ISSN：0253-6102
年,卷(期)：2024.76(5)
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