Labs 3-4: SHO and onset of anharmonicity
Simple harmonic motion and the effect of damping

Set up the iOLab remote between two springs, free to oscillate vertically (use the more rigid spring on top, attach it to the top nail, and then nail the bottom nail while stretching the weaker spring at the bottom until it is the same length as the top spring). To explore damping, come up with an air brake device (a cardboard disk?) that can be taped to the remote in two different orientations, thus providing two different air resistance regimes.

For analysis, sho.pcm is the file we developed during the lab. If you do not yet have a sample data file, you can use this: damped.txt Be sure to provide the description and/or diagrams or photographs of your set-up, clearly describing the procedure you used. If you are using a sample data set acquired on an air track, use the materials from the old lab manual to include in your lab report.


Exploring anharmonicity involves analysis of the amplitude dependence of the oscillation frequency. The experimental setup of two springs attached sideways to the direction of oscillation can be used to create an almost purely anharmonic oscillator. Please, review a note on anharmonicity, developed in class. This lab is traditionally done with an air track, and the approximation of \( d\approx l_0 \) is easy to realize.

Using iOLab makes it a bit more challenging. To avoid friction, we suspend an iOLab remote on two long rubber bands (provided in your kit) between legs of a chair or a coffee table, and the rubber bands are somewhat stretched by the weight of the remote even at rest. One possble experimental setup is shown here:

One possible way to analyze the data is to acquire a very long data set, watching the amplitude of oscillations slowly decay, and extract the amplitude and frequency of oscillations out of every time slice (of 2-3 oscillationsi each). The result is shown here:

If you do not yet have your own data set, feel free to develop your analysis macro code using these previously acquired data sets. Air track data [t, x(t)]: labpro12.dat, or labpro20.dat, or labpro35.dat . iOLab data [t, x(t), v(t), a(t)]: iOLab-anharmonic-02.dat or iOLab-anharmonic-09.dat.

In the discussion, compare and elucidate features of your several experiments: the [nearly] harmonic oscillator, the effects of damping using air brake[s of different sizes], the amplitude dependence of frequency for the anharmonic oscillator.