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Deriving the duffing equation?

  1. Jan 31, 2013 #1
    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 :(
     
  2. jcsd
  3. Jan 31, 2013 #2

    TSny

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    We kindly ask that you not post the same question twice. Thank you.
     
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