Lab 5: Resonance
Driven harmonic oscillator
In the lab, this experiment is done on an air track, and a computer-controlled periodic actuator is provided to add the energy to the system at a variable frequency. At home, we replace the actuator with the finger-controlled periodic actuation. To ensure a stable frequency, a metronome app is used. With a bit of practice, students should be able to maintain a steady beat, and thus deliver the energy to the system at a precise frequency set by the metronome.
Using the same setup as in Labs 3-4, suspend the iOLab vertically using two springs, but attach the lower spring to a paper clip bent as shown in the image below. The length of the loop, and therefore the amplitude of the actuation movement should be about 1cm.
Vary the frequency of actuation systematically, making smaller steps in frequency close to the resonance. when the system reaches a steady state, acquire a trace of a few oscillation, without interupting the actuation, and extract frequency and amplitude. Consult the class notes for the functional form of the resonance curve. Fit the data, and estimate the Q factor of your system. If the amplitude of oscillations becomes too high on resonance, adjust the shape of the paper clip to have a shorter actuation travel, and repeat.
The resulting graph should look something like this:
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 is in two columns, [t, x(t)], with files labelled by frequency of actuation in Hz. In all cases, the actuation amplitude was 0.01m.
- a 2019 data set:
- a 2020 data set:
Be sure to include your (annotated!)
extrema macro in the Appendix of your lab report.