Relationship between angular speed of conical pendulum and the tilt angle of its string

Relationship between angular speed of conical pendulum and the tilt angle of its string 
Introduction:
In the previous lab, we already determine the relationship between the angular acceleration and the angular velocity, and in this lab, we determined the relationship between the the angular speed of conical pendulum and the tilt angle of its string.

We are looking for relationship between angular speed and θ.
Apparatus and process: 

We need to use this stop watch to find the total time needed for 5 finished rotations, so we can find the average period(T) of each rotation.

This is the apparatus that will do the conical pendulum motion, in this picture, professor Wolf was adjusting the height of the paper until the pendulum barely touch while spinning in order to find h2.







We did 7 trials with different angular speed in total in this lab.

Hypothesis and data:
To find out the magnitude of  angular speed of the motion, we need to use the stop watch to find the period of each rotation, and convert the period(T) to angular speed(w).
w=2π/T
Then, we have to determine the angle of the string. We find the length of h1 and the length of the string l we used for the circular motion to calculate for angle θ:
We found that l=.177m, and thus θ = cos^(-1)(h1/.177)

The following is the prediction we made for the relationship between angular speed(w) and angle θ

And if the prediction is correct, the graph of w vs.  sqrt(g tanθ/r+0.62) should have a slope of 1.
The following is the data chart:

And finally, the following is the graph of w vs.  sqrt(g tanθ/r+0.62)

Conclusion:
 We have found that relationship between the angular speed and angle θ is "w∝sqrt(g tanθ/r+0.62)."
The slope of our graph is 0.9222, which is a very close number to 1, and thus our prediction was very accurate. The constant 0.2917 in the function that represent the graph exist because of the experimental error caused by the uncertainty of the measurement equipment we used. Also, the way we measure the height h2 is very inaccurate because we used only folded paper to estimate h2.