Several physical systems are described approximately by Duffing's equation ,where a, b, and c are constants of the system and F and ω1 are constants of the applied forcing function. This is a second‐order nonlinear differential equation whose complete exact solution is unknown.
Approximate solutions for the steady‐state behavior of the systems represented by the above equation are well known. The present work investigates the transient behavior in the region of the steady‐state response. The theory developed is supported by solutions using an analog computer and by experiment with an actual electrical circuit whose behavior is approximated by the foregoing equation.
Topics
Electrical circuits
REFERENCES
1.
C. F. Spitzer and R. J. Reich, “Nonlinear resonant flip‐flop circuit,” Patent No. 2,653,254.
2.
3.
G. Duffing, Erzwungene Schwingungen bei veränderlicher Eigenfrequenz (Friedrich Vieweg und Sohn, Braunschweig, 1918).
4.
J. J. Stoker, Nonlinear Vibrations (Interscience Publishers, Inc., New York, 1950).
5.
6.
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© 1956 American Institute of Physics.
1956
American Institute of Physics
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