ASYMPTOTIC STUDY OF NONLINEAR SPRING OSCILLATION WITH EXTERNAL FORCE USING THE MULTIPLE TIME SCALES METHOD

Abstract

A nonlinear spring is a type of oscillator that does not follow Hooke's law perfectly. In mathematics, this type of oscillator can be modeled in a nonlinear ordinary differential equation. Of the many discussions on oscillation models, one examines the behavior of the model when disturbed by a parameter with a very small value. In this study, a discussion will be conducted regarding the behavior of the oscillation model with external forces added to the disturbance parameters in the damping and spring stiffness terms. To observe this behavior, one of the techniques in asymptotic analysis called the multiple time scales method is used. The results of this study will show the behavior of the oscillation model with the disturbance parameters caused by the resonance that occurs. To provide a clearer picture, the oscillations that occur are presented in the form of a simulation result graph, containing a comparison between the approximate solution and the numerical solution. Based on the discussion given, it is concluded that the oscillations in the model are strongly influenced by a certain relationship between the natural frequency of the nonlinear spring and the frequency of the external force acting on the model.