Abstract
This paper reports on the jump phenomenon as seen in a geometrically nonlinear mass spring system. Analysis and simplification of the governing differential equation results in two coupled equations, which were solved in MATLAB using various values for mass of the oscillator (M), effective spring stiffness (K), mass of the flywheel (m), radius of gyration of the flywheel (r), and damping (C) of the system. Depending on values of the parameters used, various theoretical system responses were seen for the cart amplitude as a function of driving frequency. Based on the output of the MATLAB program, components were chosen to implement into a mass spring system that would physically illustrate the jump phenomenon. The result is a nonlinear spring system that was able to show the jump down effect, but not the jump up.
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