Forced Oscillators
Richard H. Enns, George C. McGuire · Birkhäuser Boston eBooks · 1997
In Maple file MF09 the student has already seen some of the exciting possible solutions which can occur for a forced oscillator depending on the amplitude F chosen for the forcing term. The nonlinear system in that file is the Duffing oscillator (7.1) $$ \ddot x + 2\gamma \dot x + \alpha x + \beta x^3 = F\cos \left( {\omega t} \right) $$ with γ the damping coefficient and ω the driving frequency. In mechanical terms, the lhs of the Duffing equation can be thought of as a damped nonlinear spring. With the forcing term on the rhs included, the following special cases have been extensively studied in the literature: