Using the formula for a rigid pendulum.

[ardnassac.95]

How to use the formula for a rigid pendulum?

Given the formula T = 2π√(2L/3g)
(1) how do you change to get T^2 = ?
(2) And then how (1) to get g = ?

Here's what I've tried, but I'm not sure if they are correct:
(1) T^2 = 4π^2 x (2L/3g)
(2) g = [4π^2 x (2L/T^2)] ÷ 3

(3) The experiment is to find the relationship between length of rod, L and period, T, for a rigid pendulum (i.e rod) hooked onto a stand. When we plot the transformed data onto a graph it should be L vs T^2, but the formula in (2) as I've tried above give 2L/T^2 not L/T^2 as given as the gradient of my graph. So how would I use the gradient to put into the formula (2) to get g (gravity) which should be 9.81ms^-2? Do I double my gradient and substitute that as 2L/T^2?

 

[lippyka]

Yes, you should double your gradient and substitute that as 2L/T^2. Once you have done that, you can solve for g by rearranging the formula to get g = [4π^2 x (2L/T^2)] ÷ 3.