We performed an experiment in which we turned a bicycle on its side and placed a piece of green tap on one of the spokes. We spun the wheel and recorded the wheel spinning until it came to a complete stop. A stop watch was in the frame of the video so we could note each time that the wheel completed one revolution, so we could calculate the angular velocity. For example, the green tape made on complete revolution in .6 seconds, and 2 revolutions in 1.31 seconds, 3 revolutions in 2.19 seconds, etc. So my question is, how do I go about graphing this to determine if the wheel is undamped, under damped, or over damped. I am having a hard time thinking of a way to plot the data to replicate some sort of oscillation. I may be wrong, but I calculated the arc that the wheel traveled as a function of time, synonyms to a position vs time graph, in order to view the response of my systems but clearly that doesn’t produce an oscillating graph. As time goes on, the arc distance traveled (s) is always getting larger until the wheel stops. Examples I see, shows the displacement vs time graph of a spinning wheel but I don’t understand how can the displacement initially goes up and then come down, and then rise again and produce an isolating motion. That is easy for me to imagine for a spring mass, because the motion is literally swaying back and forth but in the case of a wheel, the distance is always getting larger.

We performed an experiment in which we turned a bicycle on its side and placed a piece of green tap on one of the spokes. We spun the wheel and recorded the wheel spinning until it came to a complete stop. A stop watch was in the frame of the video so we could note each time that the wheel completed one revolution, so we could calculate the angular velocity. 

For example, the green tape made on complete revolution in .6 seconds, and 2 revolutions in 1.31 seconds, 3 revolutions in 2.19 seconds, etc. 

So my question is, how do I go about graphing this to determine if the wheel is undamped, under damped, or over damped. I am having a hard time thinking of a way to plot the data to replicate some sort of oscillation. 

I may be wrong, but I calculated the arc that the wheel traveled as a function of time, synonyms to a position vs time graph, in order to view the response of my systems but clearly that doesn’t produce an oscillating graph. As time goes on, the arc distance traveled (s) is always getting larger until the wheel stops. 

Examples I see, shows the displacement vs time graph of a spinning wheel but I don’t understand how can the displacement initially goes up and then come down, and then rise again and produce an isolating motion. That is easy for me to imagine for a spring mass, because the motion is literally swaying back and forth but in the case of a wheel, the distance is always getting larger.