Is This the Correct Method for Deriving the Duffing Equation?

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SUMMARY

The discussion focuses on deriving the Duffing equation for a mass-spring-damper system. The user correctly identifies the restoring force as F = -kx + x^3, incorporating damping as bx' and applying Newton's second law. The final equation presented is mx'' = -kx + x^3 + bx' + Fcos(wt), which accurately represents the dynamics of a driven nonlinear oscillator. The user seeks confirmation on the correctness of their derivation, particularly regarding sign conventions.

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  • Familiarity with nonlinear dynamics and the Duffing equation
  • Knowledge of damping in mechanical systems
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Say I have a mass m on a non linear spring k with some damping b.

I start with the restoring force of the spring F=-kx+x^3... the x^3 is the non linearity.

Set that equal to Newtons second law F=mx'' = -kx+x^3

Add in the damping which is dependent of velocity bx'

......mx'' = -kx + x^3 + bx'
......= x'' + k/m*x + x^3 + bx'
......= x'' + bx' + w0*x + x^3... Now because my system is driven I add in a periodic force dependent on t.

Fcos(wt) = x'' + bx' + w0*x + x^3

Is this the correct method? I may have gotten mixed up with my signs I tend to do that :(
 
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