Simple Harmonic Motion: Period Dependence on Variables and Curve Fitting

[wizzpowa]

Homework Statement

I'm doing a lab, and they want me to show the dependence of the period on different variables (displacement, mass, and length of pendulum). They ask me to "Fit curves to your plots to show the dependence. Use the curve fits from your plots to devise an equation for
determining the period of oscillation for a simple pendulum," and then to "Compare your
equation to the standard equation for a simple pendulum."

So my questions are:
-How do I fit a curve to my graphs (i'm using logger pro), and what information can I get from doing that?
-What is the equation for the oscillation of a simple pendulum? All I've found is the one for angles smaller than 1 degrees. Thanks!

Homework Equations

The only equation I have found online is T= 2 pi sqrt (L/g)

The Attempt at a Solution

 

[Erbil]

-the differential equation for simple pendulum is ;

md^2x/dt^2=-mgsinβ if we choose small angle it will simple harmonic motion.

IF the length of the rope is L , and displacement is x;
we can write sinβ=x/l

from our differential equation md^2x/dt^2 = -mgx/l /divide both side to m
d^2x/dt^2=-(g/l)x

we know that; a = -ω^2(x)

ω=(g/l)^1/2 from this expression we can say that period is T=2∏(l/g)^1/2

It's means that you have to try with different size of rope.Simple pendulum depence only size of rope.