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abaset
Joined: 13 Feb 2009 Posts: 2 Location: Singapore

Posted: Thu Feb 19, 2009 5:54 pm Post subject: Damping in Duffing drivenanharmonic oscillator 


Greeting every one.
In Duffing equation, the damping coeffecient usually assume possitive values (<<1). However, at certain cases, the damping coeffecient may asume negative values.
Can any one explain the meaning of positive and negative damping in Duffing equation as well as in real physical systems.
Further, in modelling the nonlinear response of a nonlinear material driven by optical laser source using Duffing equation, what type of damping we have in this case.
any contribution is appreciated. 

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hepcj Site Admin
Joined: 23 Jun 2007 Posts: 125

Posted: Wed Feb 25, 2009 12:16 am Post subject: 


The Duffing oscillator is the same as a normal Forced oscillator with damping, however, it has nonlinear restoring force term.
x''(t) + delta x'(t) + F(x[t]) = A cos(w0 t) where
F[x(t)] =  alpha x(t)  beta x(t)^3
The nonlinear part is in the constant beta, for beta=0 it reduces to a linear second order differential equation.
In any case the damping factor beta >=0. If it were negative it would correspond to the addition of energy rather than a dissipation of energy from the system.
In an optical system, this might be a hint at amplification but I am not certain. 

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