The research involves experimental analytical and theoretical methods in the study of chaotic vibration in a nonlinear system described by Duffing's equation. Emphasis is on nonlinear vibration analysis. Energy concepts are explored as a way to derive chaotic criteria. The relationships are investigated between the energy levels of the states of periodic motion and the equation parameters: damping, and the amplitude and frequency of the forcing function. This project is one supported under the Creativity Awards for Undergraduate Engineering Students.