Bifurcation and Nonlinear Oscillation of the Bead Motion

TL;DR

This paper investigates the bifurcation and nonlinear oscillations in a bead-hoop system through theoretical modeling and experiments, revealing complex dynamic behaviors and stability changes.

Contribution

It provides a quantitative theoretical model of the bead-hoop system and experimentally validates bifurcation and nonlinear oscillation phenomena.

Findings

Identification of pitchfork bifurcation in the system

Experimental confirmation of nonlinear oscillations

Analysis of errors in experimental measurements

Abstract

This research focuses on the interesting physical phenomenon of the bead-hoop system. The bifurcation can be observed investigating the equilibrium point of the bead, and nonlinear oscillation also occurs from the bead's motion. This paper includes the theoretical investigation by setting the quantitative model and studying pitchfork bifurcation. Also, the equation of motion is derived by investigating resistance. Three parts of experiments were done and went through analysis by examining standard error, error of experiment, and the error of fitting.