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Homework Help: Lagrange Function for a certain problem

  1. Dec 16, 2011 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m is connected by a massless spring of force constant k and unstressed
    length r0 to a point P that is moving along a horizontal circular path of radius a at a
    uniform angular velocity ω. Verify the Lagrange-Function!

    2. Relevant equations

    Could there be a typing error in the book (the book provided the solution which can be seen in the file "function.png". My own solution just differs in the term with r and has 1/2*m*r^2*theta' instead of 1/2*m*r*theta' like shown in the book. However i think my solution is right or can anybody find a mistake?

    3. The attempt at a solution

    x[1](t):=a*cos(omega*t)#`this is the x-coordinate of P
    y[1](t):=a*sin(omega*t)#`this is the y-coordinate of P
    x[2](t):=x[1](t)+r(t)*cos(theta(t))#`this is the x-coordinate of m
    y[2](t):=y[1](t)+r(t)*sin(theta(t))#`this is the y-coordinate of m
    T := (1/2)*m*((diff(x[2](t), t))^2+(diff(y[2](t), t))^2)
    V :=(1/2)*k*(r-r[0])^2

    I attached a drawing of the exercise and two lagrange functions (from the book and my solution) and a Maple file for convenience.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution

    Attached Files:

  2. jcsd
  3. Dec 17, 2011 #2


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    Science Advisor
    Homework Helper

    Your answer is almost certainly correct. That term in the books answer doesn't have consistent dimensions with the terms around it.
  4. Dec 17, 2011 #3
    Ah yeah. I should have checked the dimensions as well! Thanks for the advice!
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