How do I rearrange t^2 = 4pi^2 L/g in y=mx format?

Question

T² = 4πi² L/g

How do I derive formula to make:

L = y

T² = x

4πi²/g = m ?

so far I have :

L / T^{2 =} g x 4π²

Is this correct ?

Answer 1

As far as I understand, you took the formula for the period of the pendulum and want to put it in a way so, that you could find g and use linear graph for this.

You already wrote that

L / T² = 4π²g

From here

g = 1 / 4π² (L / T²)

At first you plot the graph L vs T² . You put T² on horizontal axis and L - on vertical. Then you need to find the slope of this graph (tan of the angle between the graph and horizontal axis).

Now you can write

g = 1 / 4π² x Slope

Hence, if now you divide the slope of the graph by 4π² , you will get the experimental value of the acceleration due to gravity g. And you are done.