The transient response of second order non-linear equations

A method is presented for calculating the transient response of second order non-linear differential equations. The increase in accuracy over such methods as the Kryloff-Bogoliuboff technique, physically speaking, is due to the inclusion of the phase-lag effects caused by the linear damping term in the equation. Mathematically the increase in accuracy is obtained by an appropriate choice of the zero-th order terms for the dependent variable and its first derivative. This inclusion requires little more calculation effort than that required in the Kryloff-Bogoliuoff technique. Additionally, this method may be iterated to obtain solutions of increased accuracy ; the next higher order solution being carried out in detail in the text. Examples are presented to show the increase in accuracy of the present method over the Kryloff-Bogoliuboff technique.