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Damping in Duffing driven-anharmonic oscillator

 
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abaset



Joined: 13 Feb 2009
Posts: 2
Location: Singapore

PostPosted: Thu Feb 19, 2009 5:54 pm    Post subject: Damping in Duffing driven-anharmonic oscillator Reply with quote

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

PostPosted: Wed Feb 25, 2009 12:16 am    Post subject: Reply with quote

The Duffing oscillator is the same as a normal Forced oscillator with damping, however, it has non-linear 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 non-linear 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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