PERIODICITY IN A HARMONICALLY EXCITED DAMPED PENDULUM

We study, in this paper, the nonlinear dynamics of a damped and forced pendulum. This simple model can represent robotic arms, antennas and space solar panels, energy harvesting devices of vibrations present in waves etc. The response of this system has a wealth of possible behaviors, depending on model parameters, initial conditions and the amplitude and frequency of loading. The answers may result periodic, of several different periods, almost periodic, chaotic etc. This work intends to make a numerical parametric study. The problem is mathematically modeled by an ordinary differential equation obtained by Newton's laws. The evaluation of the response and the characterization of its stability is given by numerical integration of thismathematical model by Runge-Kutta 4th order algorithm, implemented in MATLAB environment. In this paper, we show an interesting aspect of the dynamic behavior of this model, namely periodic damped free vibration responses depending on certain parameters and initial conditions. Some preliminary periodic forced responses are also shown. Keywords: Nonlinear dynamics, damped and forced pendulum, periodic behavior