(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Homework Help: Rigid Pendulum g derivation equation

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