A question on Pendulum experiment

[jmnk]

The program "Acceleration Spectrum" in "Tools" presents FFT of all accelerations components together. For studies of a pendulum it is interesting to separate them. So I give slightly modified version "Acceleration Spectrum 2" where ax (red), ay (blue) and az (yellow) are separated and presented in the same graph. The results for illustration are obtained with my, fortunately conserved, pendulum with smartphone put at the bob position with x-axis in the direction of motion and y-axis in the direction of the pendulum rod. One can easily see the primary frequency 0.5 Hz of the pendulum for ax and a double frequency for ay. The effect is many time discussed in the literature and recently becomes the topic of a special paper: Sophie Reinhold and Michael Ziese 2020 Eur. J. Phys. in press https://doi.org/10.1088/1361-6404/abc2db.

Many thanks for all your help.  I've just tried that new experiment that you have provided - but on the 'spectrum' view I get (I think) all three acceleration components in the same color so it is not possible to distinguish each component.  I loaded that experiment via downloading your .phyphox file on my PC, then loading it into phyphox editor, creating a QR code, and then letting phyphox app on my phone load that experiment from that QR code.  I think it all worked since the title does say 'Acceleration Spectrum 2'.  Any ideas?

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The resolution in the autocorrelation graph corresponds to that of the sensor, so for iDevices it would be 100Hz, i.e. one dot each 10ms. The analysis algorithm looks out for the right most maximum and divides the time shift by the order of the maximum. This improves the resolution a bit to 10ms/order.

I performed a few tests and could definitely see a 10ms “grid” in 1/frequency, i.e. the period. The associated order of the dots in-between keeps me wondering a bit (in the final example one less than expected)…

Jens,
thank you so much for your help.  I'm not sure if I fully follow, so let me try in my own words. referring back to my screenshot.  Are you saying that:

• data points marked in blue and in green are there because while the frequency of the pendulum changes continuously, the fact that the sensor is of finite resolution makes the results appear as there are two distinct resonance frequencies.  Because some data points will result to (round off to) resonance frequency ~0.83Hz, while others to ~0.8356Hz.  That would make perfect sense to me.
  
• data points marked in red - it is still a bit unclear why these are there?
  

Now, judging from that one would expect the frequency of the pendulum reported in that experiment to fall somewhere in [0.83Hz, 0.8356Hz] - because majority of of data points are in that range.  But in that run the value provided was 0.84Hz.  As if the value was rounded up?  Maybe I'll try to modify the experiment so it reports the value (in the autocorrelation and results view) with more than 2 decimal digits precision and see what happens.