The notebook I developed serves more as a tool, as well as a sensor or a caliper,
to acquire accurate data from physics experiments, the latter being the real target
of study. In other words, after capturing the movement data, the student must perform
all the analysis, which, in my course, involves curve fitting from mathematical models
to experimental data. The case illustrated in the notebook outputs is just an example
applied to the case of the damped pendulum launched from high angles. But this
notebook can be used for many other experiments.
A: Of course versatility of automated analysis is desirable, but I found that refinement of experimental design was also necessary to get good results beyond simple harmonic oscillation.
To be clear: There really is no point in extracting a damping coefficient, because it is only relevant to engineering and fault tolerance. Aside from characteristic frequency, the period-energy function has about one more degree of freedom, so I think you should study my Chapter 2 to see an example how shape parameter extraction can be done. If the shape parameter is extracted correctly, we say that we have verified Euler's monumental elliptic integral.
So you also have to worry should it be a bob on a string or a weight on a solid rod. I found a cheap solution with a fidget spinner worked well enough. Here's one run, not necessarily the best. In my notebooks I have some neat tricks that I haven't shown off, which have to do with data extraction and transformation to get such a pretty result at the end.
If you are studying my dissertation--I request and encourage that you do--please make sure to understand the figures 2.15 thru 2.19. Try to surpass that if you can, because it is as high or higher than whatever European standards.
In the end we could hope to get data for the three other special cases in Chapter 3, but that is going to take some creative thinking and creative experimental design... could be a good PhD project for a fan of Caetano Veloso.
