Multiple scales method for analyzing a forced damped rotational pendulum oscillatorwithgallows  

作　　者：Haifa A Alyousef Alvaro H Salas B M Alotaibi S A El-Tantawy 

机构地区：[1]Department of Physics,College of Science,Princess Nourah bint Abdulrahman University,P.O.Box 84428,Riyadh 11671,Saudi Arabia [2]Department of Mathematics and Statistics,Universidad Nacional de Colombia,FIZMAKO Research Group,Colombia [3]Department of Physics,Faculty of Science,Port Said University,Port Said 42521,Egypt [4]Research Center for Physics(RCP),Department of Physics,Faculty of Science and Arts,Al-Mikhwah,Al-Baha University,Al-Baha 1988,Saudi Arabia

出　　处：《Communications in Theoretical Physics》2024年第5期58-67,共10页理论物理通讯（英文版）

基　　金：funded by the Deanship of Scientific Research,Princess Nourah bint Abdulrahman University,through the Program of Research Project Funding After Publication,grant No(44-PRFA-P-107).

摘　　要：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.

关 键 词：rotational pendulum system multiple scales method approximate solution damped oscillations forced pendulum with gallows he-multiple scales method 

分 类 号：O32[理学—一般力学与力学基础]