Circular Motion: Radial Distance vs. Period of Rotation

[Thereheis]

Homework Statement

This is not like a wheel where distance does not matter because a particular point will pass at the same time no matter how far down or up the wheel.

In this experiment, I used a string attached to a stopper (at the top) with a washer (on the bottom). There was a glass tube that I put the string through so I could place a piece of tape to indicate length. The piece of tape would help me keep a constant speed (if it moved I wasn't keeping a constant speed). I took down trials and recorded the period of rotation and the length that I had used.

Now what I am really getting to is this: Because my data wasn't completely linear, my teacher asked me to make a "calculated variant of my variable that best approximates a direct proportion." (Length vs. Period of Rotation)
and second
To derive the theoretical relationship between the period and my assigned variable (radial distance). Mass was constant

Period of Rotation and Length (cm)- .723 Length 31, .860 Length 41, .981 Length 45, 1.089 Length 57, 1.480 Length 62.

I am having trouble with the first one because we didn't use a mass. I've worked equations a lot to try and figure out what makes the Period directly proportional to the Radial Distance (I always end up with two unknowns, but I have to find the value for radial distance that makes it linear).

Homework Equations

Circular Motion Equations

The Attempt at a Solution

For my second part of the question I have it figured out i think:
M=mass of stopper m=washer
r=Mv^2/mg

 

[Carid]

Your description of your experimental setup is not at all clear to me. Perhaps a diagram would help.

 

[Thereheis]

Thanks for replying:

I think I've got it, the one thing I am stuck on is whether Radial Distance is Directly proportional to the Period of Rotation. If these two are directly proportional, does that mean they are each directly proportional to velocity as well? How do I figure the direct proportion?