Forced Oscillators

  • Richard H. Enns
  • George C. McGuire


In Maple file MF09, the student has already seen some of the exciting possible solutions that 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
$$ \ddot{x} + 2\gamma \dot{x} + ax + \beta {{x}^{3}} = F\cos (wt) $$
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:
  1. 1.

    Hard spring Duffing oscillator: α > 0, ß > 0

  2. 2.

    Soft spring Duffing oscillator: α> 0, ß<0

  3. 3.

    Inverted Duffing oscillator: α < 0, ß > 0

  4. 4

    Nonharmonic Duffing oscillator: α = 0, ß< 0.



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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Richard H. Enns
    • 1
  • George C. McGuire
    • 2
  1. 1.Department of PhysicsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of PhysicsUniversity College of the Fraser ValleyAbbotsfordCanada

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