The aim of this study is to show that numerous configurations can be obtained with such a simple thing that is a pendulum. Indeed, with only a mass attached to a rod, it is possible to produce chaotic behavior.
In this study, it has been chosen to use a damped and driven pendulum.
In general, different damping mechanisms of different strengths are possible. Here, the main sources of damping are aerodynamical friction due to the motion of the mass through the air. They are modeled as a linear function of the speed.
By the same way, there are several ways to drive a pendulum. The simplest (and the chosen) one is to add a periodic force.
After reminding the motion equations of the pendulum and explaining the choice of the numeric scheme to solve the equation, a presentation of the phase graphs which can be obtained for the different pendulum (simple, damped and driven) is done. Then you will be able to find by yourself the different configurations given by such a pendulum by using an applet or the MATLAB programs developed for the need of this study.