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B Non - Harmonic Motion

  1. Aug 25, 2016 #1
    If the Pendulum doesn't follow Harmonic Motion can we still use the formula

    1) T = 2π Root(L/g) ?????

    2) If not, how can I calculate gravity g?
     
  2. jcsd
  3. Aug 25, 2016 #2

    Krylov

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    1) No, this is only true in the small angle approximation.
    2) You could simply start from a small angle, so the amplitude-independent formula for the period holds. If you insist on starting from an arbitrary angle, you need to deal with an elliptic integral, see e.g. here. There is a lot of literature on this topic, but if your purpose is to find the value of ##g##, other methods are perhaps better.
     
  4. Aug 25, 2016 #3
    Thank You !!!! :)
     
  5. Aug 25, 2016 #4

    Krylov

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    In fact, upon closer inspection, it does not seem too hard to determine ##g## starting from a large angle either. If you have a look at that Wikipedia-link I gave and you go to the section "Arbitrary-amplitude period", you can see that ##T## is the product of ##4\sqrt{\tfrac{\ell}{g}}## and an elliptic integral that depends on ##\theta_0## (the amplitude), but not on ##g##. So, if in your experiment you measure ##\theta_0## and ##\ell## and then compute the elliptic integral numerically (or from a table) using your measured value of ##\theta_0##, you can determine ##g## this way.
     
  6. Aug 27, 2016 #5
    Thank you soooooooooooooooo much !!! :) :)
     
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