Abstract
We present a method for estimating the power spectral density of the stationary response of the simple pendulum consist of a mass m, approximated here as pointmass which is attached to the lower end of light, rigid rod, of length l. The upper end of the rod is free to pivot about point, at 0. If attention is restricted to oscillation of the pendulum in a vertical plane the one has a single degree of freedom system, approximately. Numerous applications of this technique for studying the response of non-linear oscillators to random excitation have described in the literature (Roberts, Spanos). An equivalent linear system is derived, from which the power spectral density is deduced. The theoretical analyses are verified by numerical results.
Keywords: Duffing Oscillator, Random Vibration, Power Spectral Density