The Variable Mass- Spring System and the Bessel's Function

Salleem  Ahmeda; Fawzi Ikraiam

doi:10.51984/jopas.v22i3.2771

Basic Sciences

Salleem Ahmeda ⁽¹⁾ , Fawzi Ikraiam ⁽²⁾

(1) Physics Department, Faculty of Science, Omar Al-Mukhtar University, EL-Beida, Libya ,

(2) Physics Department, Faculty of Science, Omar Al-Mukhtar University, EL-Beida, Libya

https://doi.org/10.51984/jopas.v22i3.2771

Issue
Vol. 22 No. 3 (2023): Sixth International Conference on Science and Technology

Submitted
October 18, 2023

Published
October 2, 2023

Keywords:

Mass-spring system, Bessel's function, damped harmonic oscillator, variable mass, adiabatic invariance

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Abstract

Damped harmonic oscillator and Bessel’s function both exhibit similar behaviours. In order to justify this similarity between the two functions, the mass-spring system with variable mass is used. It is shown how the damped harmonic oscillator can be used as an approximated function for the Bessel function. The adiabatic invariance is also employed to make the mathematical and physical comparison between the two functions. It is also shown how to use the zeros of the Bessel's function to obtain the same approximation by solving the boundary-value problems. The zeros of the Bessel's function are used to calculate the time period of the variable mass-spring system.

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Authors

Salleem Ahmeda

Physics Department, Faculty of Science, Omar Al-Mukhtar University, EL-Beida

Fawzi Ikraiam

Physics Department, Faculty of Science, Omar Al-Mukhtar University, EL-Beida

fawzi.ikraiam@omu.edu.ly (Primary Contact)

Ahmeda, S., & Ikraiam, F. (2023). The Variable Mass- Spring System and the Bessel’s Function. Journal of Pure & Applied Sciences, 22(3), 197–200. https://doi.org/10.51984/jopas.v22i3.2771

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