ANALYSIS OF PERIODIC SOLUTION ON NONLINEAR OSCILLATOR SYSTEMS - Mubarok, Nahrul
Oscillator is a tool that is widely applied in everyday life because of its ability to produce oscillatory motion without the need for continuous external force. To obtain the desired oscillatory motion, it is necessary to analyze the bifurcation external force parameters of the oscillator system. The resulting oscillatory motion can be viewed as an isolated periodic solution of the system of differential equations, which is modeled by oscillator system. In this final project, we will look for a method to find the periodic solution of an oscillator equation. This method finds the periodic solution with a nonlinear external force that depends on the speed of the oscillator load. Numerical integration can be used to find periodic solutions by integrating until the amplitude of the solution does not change significantly. The periodic solution can also be found by using the root-finding method of the scaled oscillator equation. This method is suitable for finding the period of the periodic solution of the oscillator equation if the period does not appear explicitly in the equation. The linear stability of the periodic solution can be found using Floquet’s Theorem. The numerical continuation method can be used to replace iterations on the bifurcation parameters. This method is effective when the drawn orbit has an inflection point. By using these methods to draw a bifurcation diagram, the behavior of the oscillator system under review can be categorized into three parts with respect to changes in the linear damping parameters.