1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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 :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Lagrangian equation for unconstrained motion
  1. Unconstrained motion (Replies: 2)

Loading...