Rigid Pendulum g derivation equation

[TOPOG]

Rigid Pendulum "g" derivation equation

Homework Statement

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)

Homework 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

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 that's my final answer

 

[TOPOG]

taken from following lab

http://courseweb.edteched.uottawa.ca/phylab/Pdf/Pdf_win/Gen/Exp 04 h2008 pdf.pdf