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Rigid Pendulum "g" derivation equation
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)
(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
- 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
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