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       The properties and behaviors of oscillatory systems are often studied in physics, but rarely are the systems fully described with the physical constants when nonlinear effects are involved.  This study presents experimental results from three different oscillating systems: an LRC circuit, a “chaotic pendulum”, and a torsion pendulum.  Period doubling, quadrupling, octupoling, and finally, chaotic behavior were observed.  The chaotic pendulum produced nice Poincaré sections, a special way to view the chaos phenomenon.  The torsion pendulum made it easy to determine all associated physical constants using analytical experiments.  After finding the spring constant, moment of inertia, and damping coefficient, the system was fully described using it’s nonlinear differential equation.  Each pendulous system produced potential energy wells which were studied.  Additionally, the effects of damping and driving were explored using the chaotic and torsion pendulums.

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