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Harmonic oscillation, spring not attached to center of mass

  1. Oct 21, 2007 #1
    A bar is guided so that one end moves on a vertical line and the other on a horizontal line. A spring is attached to the upper end according to the figure. Any friction is neglected.


    I want to find out how x varies in time. If the center of mass would have been at x and k is the spring coefficient and m the mass, then

    [tex]x = A sin (\sqrt{k/m}t + \phi_{0})[/tex]

    But now the center of mass is at the center of the rod (with length d) instead. More specifically:

    [tex]\overline{CM} = (x/2, -\sqrt{d^2 - x^2}/2[/tex]

    How does this affect the equation of motion? Is it perhaps still the same? My intuition tells me something would change when the spring isn't attached at the COM but i don't know what and why. Thankful for help!
    Last edited: Oct 21, 2007
  2. jcsd
  3. Oct 21, 2007 #2

    Meir Achuz

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    This problem is easiest with Lagrange's equations.
    If you don't know them, write a good free body diagram.

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