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

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.