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How to simplify

  1. Dec 10, 2005 #1
    I have to find out how to make this simplification
    [tex]2\pi \sqrt{ \frac {Ml^2+2Mr^2/5+m(l-r)^2/3} {(Ml+m(l-r)/2)g}} \approx 2\pi \sqrt{\frac{l}{g}(1+\frac{2r}{5l}-\frac{1m}{6M})}[/tex].:surprised :surprised

    This is for a project I have to do, but I have never done any such simplifications before. I don't know which parts of the equation are important and which aren't. If it helps this are the values of the variables:

    [tex]M\approx10kg[/tex]
    [tex]m\approx20g[/tex]
    [tex]l=227cm[/tex]
    [tex]r=6cm[/tex]
     
  2. jcsd
  3. Dec 10, 2005 #2

    Astronuc

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    Staff: Mentor

    [tex](Ml+m(l-r)/2)g[/tex] would simplify to ~Mlg, in the denominator under the root.

    (l-r)2 would simplify to l2 for very small r, otherwise l2-2rl since r2 would be small.

    r/l = 6/227 = 0.026

    m/M = 0.02/10 = 0.002 so M-m ~ M is a good approximation.
     
  4. Dec 12, 2005 #3
    Thank you.
     
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