T( period) Vs. L (length) Interpretation

[knowLittle]

Homework Statement

Now , analyze the data with a power function least square fit. Let the x values be the length and the y value be the period.

From the results of the power fit, compare the experimental value of the period to that calculated USING THE POWER FIT YOU JUST DETERMINED.

Homework Equations

The power fit equation is of the form: f(x)=a x^b

T= 2 pi SQRT(L/G)

The Attempt at a Solution

I have to shape the known equation of T to the power fit form f(x).

Could someone help?

 

[AvroArrow]

The power fit equation is of the form: f(x)=a x^bSo, we can rewrite T as: T= 2 pi SQRT(L/G) => T = 2 pi (L/G)^(1/2) => T = 2 pi L^(1/2) G^(-1/2) => f(x) = 2 pi x^(1/2) G^(-1/2) => f(x) = a x^b => a = 2 pi G^(-1/2) => b = 1/2 Therefore, the power fit equation is: f(x) = 2 pi G^(-1/2) x^(1/2)