"It may happen that small differences in the intitial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible." -Henry Poincaré, 1913 (Baker 1).
The phenomenon known as chaos is most frequently described as a "sensitive dependence on intial condition" (Moon 4). Chaos in no way implies an indeterminate system. On the other hand, chaos describes a system which, although it is determined completely by natural laws, cannot be predicted to the exponetial growth of error. In recent years, the study of chaos has been quite popular as it has been observed in dozens of systems including weather patterns, vibrations in structural beams, the stock market, fluid dynamics, electrical circuits and many more.
These pages describe a study of chaos in a damped and driven physical pendulum, a system which provides an excellent, understandable introduction to chaos. Our pendulum system contained a small disk with edge mass, a linear spring force, and an electric driving motor. This study includes the theory behind linear, non-linear, and chaotic dynamics as well as mathematical models of the chaotic pendulum. In the data section, we explain our results using phase space portraits. It is well known that chaotic systems exibit a fantastic mathematical structure described as fractals. This topic is discussed in the Mathematical Modeling section.