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Homework Help: Free Fall with Viscous Friction

  1. May 10, 2013 #1
    Hello, First post hear so bear with me.

    I have a mass in free fall with a viscous friction which can be derived from the dissipative potential Kv2/2. I must find the Lagrangian and proove that the maximum speed is v=mg/K. I have the following Lagrangian:


    When I do the Euler-Lagrange:


    However, from this equation I cant proove that maximum velocity.

    Any help will be appreciated.
    Last edited: May 10, 2013
  2. jcsd
  3. May 11, 2013 #2

    George Jones

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    I you sure "dissipative potential" was used in the question? Did you use the Euler-Lagrange equation that is appropriate for dissipative systems?
  4. May 11, 2013 #3
    Hello, the question does say "Dissipative Potential". From what I've seen in class, if the force can be derived from a potential, the normal Euler-Lagrange equations are still valid. Therefore I used the following:



    [itex]\frac{\partial \mathcal{L}}{\partial y}-\frac{d}{dt}(\frac{\partial \mathcal{L}}{\partial \dot{y}})=0[/itex]

    And I get:




    I think my problem is with the dissipative potential. How do I deal with it?
  5. May 11, 2013 #4

    Jano L.

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