Bifurcation and Nonlinear Oscillation of the Bead Motion

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.