Assessment of the behavior of weakly and highly nonlinear friction-driven oscillatory systems

The behavior of weakly and highly nonlinear oscillatory systems driven by friction is investigated in this work with the approximate and numerical solutions developed via a piecewise-constant approach. The solutions developed for the systems are continuous everywhere on the time range desired. It is found in the research that the properties of the weakly and highly nonlinear systems exhibit great differences, though the governing equations of the two systems employ identical system parameters. The approximate solutions developed can be conveniently implemented for the purpose of analytically and numerically studying the properties of the system with numerous system parameters and various initial conditions. The highly nonlinear system is found physically much involved and its behavior is much complex in comparing with that of the weakly nonlinear system. Based on the approximate solutions developed for the highly nonlinear system, recurrence relations are generated for numerical calculations.