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Homework Help: Quick pendulum question

  1. Oct 22, 2004 #1
    How would the period of a pendulum change if A)the string's mass was negligible and b) the stings mass had to be accounted for. I can think of arguments for both but can't find an equation or definate answer for either one.
    I think the period will increase since I=I(string)+ml^2 and the period equals T=2pi*sqrt(I/mgl)
    Help please!
    Last edited: Oct 22, 2004
  2. jcsd
  3. Oct 22, 2004 #2


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    Science Advisor

    If the string's mass was not negligible, in comparison to the "bob", where would the center of mass be? How does the period depend upon the length of a pendulum?
  4. Oct 22, 2004 #3

    Doc Al

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    Staff: Mentor

    The period of a physical pendulum is given by:
    [tex]T = 2 \pi \sqrt{I/mgl_{cm}}[/tex]
    If we include the mass of the string: I increases, of course, but so does m; but the length (from pivot to center of mass) decreases. To find out which effect dominates, you'll have to plug in expressions for I, m, and l and then compare the period to that of a simple pendulum without the string's mass.

    According to my analysis (do it for yourself), if you include the mass of the string, the period would slightly decrease.
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