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Lagrangian Mechanics - Pendulums and a Spring.

  1. Oct 17, 2008 #1
    1. The problem statement, all variables and given/known data
    Two masses m1 and m2 are suspended from identical strings of length L1. The strings are attached a distance L2 apart to a horizontal support. A spring (k) for relaxed length L2 is attached between the two masses. Find the equations of mtion for this system if all parts are constrained to move in a vertical plane.

    2. Relevant equations

    3. The attempt at a solution

    I believe my work to this point is correct, but I can never be 100% sure. My main problem seems to be with dealing with the x distance of the string in the 1/2k(x)^2 part. I have drawn out a second diagram to try to get a better understand of what this "stretched value" is.

    Thanks for any help

  2. jcsd
  3. Oct 21, 2008 #2
    Are you able to take the two different pendulums and use seperate polar coordinates on them for this problem? Also, I'm still having trouble with the spring stretch distance, which is needed in the potential for the langrangian. Any clues?

  4. Oct 21, 2008 #3

    Ben Niehoff

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    Gold Member

    You make very neat diagrams.

    Yes, you can use two sets of polar coordinates. To get the length of the spring, you'll have to do a bit of geometry. You should have an (x,y) for each pendulum, so you can just take the distance formula if you like. Or you can try to find a more elegant Greek-style solution.

    Note that you can always simply introduce a new independent variable for the spring length. Then you can relate the spring length to the two pendulum angles via an extra constraint equation.

    Either way, you will have to do geometry to get the length in terms of the angles. This is what some of my professors call "conservation of difficulty". :D
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