Harmonic balance approach to periodic solutions of non-linear jerk equations

The method of harmonic balance is applied to non-linear jerk equations, which involve the third order time-derivative. For many types of cubic non-linearities, the method yields good estimates of the period and displacement amplitude of oscillations for a range of values of initial velocity amplitude when compared with numerical solutions. Some limitations, notably the restriction to zero initial acceleration, as well as implications and possible extensions are discussed.