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Linearising compound pendulum equation

  1. Mar 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Linearise T=2pi√(K^2 + h^2)/gh K is known constant

    This is a compound pendulum equation, I want to plot some kind of formula with variable T against some kind of formula with variable H in order to find g from the gradient.

    2. Relevant equations



    3. The attempt at a solution

    so i've got T/2pi all squared times g all substituted to x, h subbed to y and k^2 subbed to constant C and I've got the equation y^2 -yx + C=0 and tried to solve for y=x+β

    I've tried implicit differentiation and it's gotten me nowhere
     
  2. jcsd
  3. Mar 9, 2012 #2

    tiny-tim

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    hi seboastien! :smile:

    (try using the X2 button just above the Reply box :wink:)
    if K is a known constant, can't you make one of the axes √(h2 + K2) ?
     
  4. Mar 9, 2012 #3
    I would have to make the axis √((h^2 + K^2)/gh ) but that is a good point.

    However, I would still like to know how I could linearise it further. I know that a taylor approximation is needed but I don't know how to, or what a value to choose
     
  5. Mar 9, 2012 #4

    tiny-tim

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    √(1 + (h2/K2) = 1 + (h2/K2)/2 + … :wink:
     
  6. Mar 9, 2012 #5
    ????????????????
     
  7. Mar 9, 2012 #6

    tiny-tim

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    if h/K is small, then √(1 + (h2/K2)) = 1 + (h2/K2)/2 + …
     
  8. Mar 9, 2012 #7
    hmmm, my only issue is that its the sqrt of K^2 + h^2 divided by gh

    it also turns out that k is the radius of gyration and I have no scales to measure the pendulum's mass. I believe I need a y=mx + c where the y intercept will be determined by k, g by m, x by T and h by y.

    is there any way of achieving this?
     
  9. Mar 9, 2012 #8

    tiny-tim

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    i'm confused :redface:

    you said that K was known :confused:
     
  10. Mar 9, 2012 #9
    That's because I thought I was allowed to measure the pendulums mass.

    Don't worry I've worked it out...finally, turns out I've been overcomplicating things.

    I'll just plot a graph of h^2 against h*T^2 the y intercept will be -k^2 and the gradient will be g/4pi^2.

    Thanks anyway.
     
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