ABSTRACT
Nonlinear oscillatory systems are ubiquitous in the natural universe. In recent years, attention has turned to the examination of nonlinear oscillators which do not have a harmonic oscillator limit. The harmonic balance method involves only algebraic and elementary trigonometric operations. In general, the first- and second-order solutions may be calculated by hand. A major tool of mathematical scientists is linearization of nonlinear equations. In general, for differential equations having periodic solutions, first-order calculations using the harmonic balance methods are easier to implement than iteration procedures. Iterative methods reduce the original nonlinear differential equations to the solution of linear, second-order, inhomogeneous differential equations. Which technique to apply for a given problem will depend on the particular system of interest.
