ANALYSIS OF THE MULTIPLE SCALES METHOD APPROACH FOR THE NONLINEAR OSCILLATION MODEL ON THE MOTION OF THE VERTICAL DIRECTION SPRING PENDULUM - Zikri, Fadilatil
In this thesis, an analysis of the behavior of a nonlinear oscillation model on the vertical motion of a spring pendulum is discussed, using the multiple scales method. By utilizing the multiple scales method, an asymptotic solution is resulted and it incorporates two-time scales: the fast time scale and the slow time scale. The fast time scale characterizes the rapid oscillations in the system's dynamic response, while the slow time scale encapsulates the system's overall changes. We analyze different scenarios in vertical spring pendulum motion, encompassing the non-resonant and subharmonic resonance cases. The asymptotic solution is then compared with the numerical solution to examine its accuracy.