Closed-Form Solutions to a Forced Damped Rotational Pendulum Oscillator

Alvaro H. Salas, Ma’mon Abu Hammad, Badriah M. Alotaibi, Lamiaa S. El-Sherif and Samir A. El-Tantawy ()
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Alvaro H. Salas: FIZMAKO Research Group, Department of Mathematics and Statistics, Universidad Nacional de Colombia, Manizales 170001, Colombia
Ma’mon Abu Hammad: Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
Badriah M. Alotaibi: Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Lamiaa S. El-Sherif: Department of Physics, College of Arts and Science in Wadi Al-Dawaser, Prince Sattam bin Addulaziz University, Wadi-Dawaser 11991, Saudi Arabia
Samir A. El-Tantawy: Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt

Mathematics, 2022, vol. 10, issue 21, 1-13

Abstract: In this investigation, some analytical solutions to both conserved and non-conserved rotational pendulum systems are reported. The exact solution to the conserved oscillator (unforced, undamped rotational pendulum oscillator), is derived in the form of a Jacobi elliptical function. Moreover, an approximate solution for the conserved case is obtained in the form of a trigonometric function. A comparison between both exact and approximate solutions to the conserved oscillator is examined. Moreover, the analytical approximations to the non-conserved oscillators including the unforced, damped rotational pendulum oscillator and forced, damped rotational pendulum oscillator are obtained. Furthermore, all mentioned oscillators (conserved and non-conserved oscillators) are linearized, and their exact solutions are derived. In addition, all obtained approximations are compared with the four-order Runge–Kutta (RK4) numerical approximations and with the exact solutions to the linearized oscillators. The obtained results can help several authors for discussing and interpreting their results.

Keywords: rotational pendulum system; damped rotational pendulum oscillator; forced damped rotational pendulum oscillator; Jacobian elliptic functions; trigonometric function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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