# Graph help on Damping effects on SHM experiment

1. Jan 28, 2013

### JamieGreggary

1. The problem

Okay. So just too briefly outline my experiment: I have a pendulum bob attached to two cardboard discs, and am testing to see how the radius of the cardboard discs effects the damping of the simple harmonic oscillator (the pendulum).

I have results (such as the one below which is off an 8cm diameter) ranging from 6cm to 22cm in diameter, producing a large spread of results between the time taken for the amplitude to diminish.

Now, what I am mainly confused about is how I could go about plotting a relationship between the circular disc radius, against time.

http://i50.tinypic.com/301oo6u.jpg

3. The attempt at a solution

I initially thought that I would just use the time taken for the pendulum to stop completely (i.e. have a 0 degree angular displacement), but this is too inaccurate as when the pendulum approaches 0, it starts to flicker between values and doesn’t stop completely.

I then thought that perhaps I could plot the circular disc radius against the time taken for the pendulum's angular displacement to reach 1 degree, as this is easy to find. However, it just sounds odd to have a set of results under "circular disc radius against the time taken for the pendulums angular displacement to diminish from 20 degrees (as this maximum the sensor can record) to 1 degrees". It doesn’t really tell us much, and wouldn’t really give us a concrete relationship to make predictions of pendulums amplitude after a time t with a circular disc of radius r.

4. Clarification
My main goal is to create a graph which will be able to quantifiably and graphically prove that as the radius of the circular disc increases, the damping effect increases. If possible, it would be nice to be able to derive an equation which allows us to make predictions of the time taken for the pendulums amplitude to decrease to say X when attached to circular discs of r.

Any ideas of what I could plot the circular disc radius against (it could even be completely different to what I have suggested)? Any help would be really appreciated!

Thank you very much! :-)

New ideas
Fit the equation y(t)=−(e^−at) * sin(ωt) to the graph, and plot the disc radius against the value of "a". Although, when fitting this to the data surely the accuracy of the function is going to be determined by the coordinate that you choose for the graph to pass through? (which I wouldn't be sure on which the optimum is)
Calculate the damping coefficient (or Q factor) - Although I'm not quite certain how you could do this from using the graph

Last edited: Jan 28, 2013
2. Jan 28, 2013

### haruspex

The data suggests an amplitude modulation at about one third the dominant frequency. You could try taking a moving average of y-squared and fit an exponential to that.

3. Jan 29, 2013

### JamieGreggary

Cheers for the response =]