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Rod-spring system

  1. Dec 13, 2014 #1
    1. The problem statement, all variables and given/known data

    magnet.png
    I'm really looking for a verification on parts a) and b), but I'll add what I did with part c) without going to into too much detail. I'm posting this question mainly due to part d). I feel that I have every part before this right, but I'm not getting any symmetric matrices.
    2. Relevant equations
    ##T=\frac{1}{2}mv^2##
    3. The attempt at a solution
    a)##U=\dfrac{mgL}{2}\cos{\phi}+\dfrac{k}{2}(x^2+L^2(\cos{\phi})^2)##
    b)##x_{cm}=x-\dfrac{L}{2}\sin(\phi)##, ##\dot{x_cm}=1-\dfrac{L}{2}\dot{\phi}\cos{\phi}##
    ##z_{cm}=\dfrac{L}{2}\cos(\phi)##, ##\dot{z_cm}=-\dfrac{\dot{\phi}}{2}L\sin(\phi)##
    ##T=\dfrac{mL^2\dot{\phi}^2}{6}+\dfrac{m}{2}(1-L\dot{\phi}\cos{\phi})##
    c) I know for part c) we can just use the Lagrangian of the system, then find the Euler-Lagrange and let the acceleration in the ##\phi## and ##x## directions be zero.
     
    Last edited: Dec 13, 2014
  2. jcsd
  3. Dec 14, 2014 #2

    vela

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    One mistake I see is the first term in ##\dot{x}_\text{cm}##. You're supposed to differentiate with respect to ##t##, not ##x##.
     
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