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Homework Help: Lagrangian equation for unconstrained motion

  1. May 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Write down the Lagrangian for a one-dimensional particle moving along the x axis and subject to a force: F=-kx (with k positive). Find the Lagrange equation of motion and solve it.

    2. Relevant equations
    Lagrange: L=T-U (kinetic energy - potential energy)

    3. The attempt at a solution
    All i really need help with is finding the potential energy in this problem. I believe that the kinetic energy is T=(1/2)*m*x', where x' is d/dt(x). I dont understand how to get the potential energy out of that force. Please help, thank you.
  2. jcsd
  3. May 11, 2013 #2

    George Jones

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    How do you go from potential energy to force?

    Do recognizes the force equation that you have been given?
  4. May 11, 2013 #3
    The force equation looks like that of a spring. But as far as I can remember, you go from potential energy to force by multiplying the force by the distance. This problem just seems weird to me.
  5. May 12, 2013 #4

    George Jones

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    Yes. What is the potential energy for a spring?

    No, it is the other way around, and also the infinitesimal version.

    Do have a textbook that you can read?
  6. Dec 10, 2014 #5
    I'm currently working on the exact same question, and using : $$-\frac{\partial U}{\partial x} = F$$ I integrated ##F=-kx## and got : $$T= \frac{1}{2}m\dot{x}^{2},U = kx^{2}$$

    Is this correct?
    Is T=(1/2)mv^2 always what you substitute in for a simple kinematics question?
  7. Dec 11, 2014 #6


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    No, that's not correct. The integral of ##x## is ##\frac 12 x^2##.
  8. Dec 15, 2014 #7
    Thank you for the correction, I was able to get the problem right :)
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