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.



Power Spectrum Fractal Dimension Strange Attractor Duffing Oscillator Jump Phenomenon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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