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Rigid Pendulum g derivation equation

  1. Mar 5, 2008 #1
    Rigid Pendulum "g" derivation equation

    1. The problem statement, all variables and given/known data

    Determine the general equation for "g" in terms of measurable quantities(M, Mbar, h, L, b, T, To, Tbar) from the following equations: (refer below)


    2. Relevant equations

    (1) T = 2pi(I / Mgh)^(0.5)

    (2) (Io / Ibar) = (To / Tbar)^(2)

    (3) Ibar = (Mbar / 12)(L^2 + b^2)

    (4) I = Io + Mh^2



    3. The attempt at a solution

    - Alright first i re - arranged eqn. (1) so that g = [ (I*4pi^2) / (T^2)] / (Mh)

    - Then i re - arranged eqn. (2) so that Io = [(To / Tbar)^(2)](Ibar)

    - I then used eqn (3) and subbed it into the new equation (2)

    Io = [(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] (5)

    - I then subbed in our newly formed eqn (5) into eqn (4)

    I = [(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2 (6)

    - Now i sub eqn (6) back into our re arranged equation for g

    g = [({[(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2}*4pi^2) / (T^2)] / (Mh)

    and thats my final answer
     
  2. jcsd
  3. Mar 5, 2008 #2
    Last edited by a moderator: Apr 23, 2017
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