Bessel Function and Damped Simple Harmonic Motion

Abstract

A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass respectively) have been used as evidence for this observation. It is shown in this paper how Bessel functions can be approximated by the damped sinusoidal function. The numerical method that is introduced works very well in adiabatic condition (slow change) or in small time (independent variable) intervals. The results are also compared with the Lagrange polynomial.

Large-scale coherent Ising machine based on optoelectronic parametric oscillator

“…Although many solutions | s 0 | satisfy Eq. ( 5 ) because the first-order Bessel function is approximately a damped sinusoidal function 48 , only the first/smallest | s 0 | is available in the proposed system. The phase solutions, , represents stable points, and , represents unstable points (see section 1 in Supplementary Materials).…”

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

“…A parametrically excited system, like the variable mass-spring system, is used as a physical model to investigate where the two set of functions agree. Then, the results of the exact solution that contain Bessel functions are studied and approximated with the solution of the damped harmonic oscillator [15]. The zeros of Bessel functions play an important role in computational mathematics, mathematical physics, and other areas of natural sciences [16].…”

Physical Motion of Mass Spring System Using MATLAB

“…Mass Spring Damper models has number of applications (Chandra, 2018) which includes control parameters estimation, robotic control , control of vibrations. (Asadi-zeydabadi, 2014;Li & Horowitz, 2001)There are number of factors responsible for damped forces. Among them are damping due to Coulomb friction, dry friction.…”