The amplitude A3 of the third harmonic in equation (16) can be estimated similarly by equating to zero the coefficient of cos 3ω1 t, when ψ from equation (16) is substituted into equation (15). It is convenient to express A3 as a function of the
amplitude A1 of the slow motion: A3 = 1 A3 /(16 − 7A2 ). The corresponding graph is
3 1 1
shown by a solid line in Figure 7. The points refer to the simulation of the subharmonic
oscillations with n = 8.