A question on Pendulum experiment

[jmnk]

I've just discovered this app - this is the most awesome!  

I have a question regarding pendulum (or spring) experiment.  I'm a bit confused about the meaning of the 'resonance' graph.  Here's my screenshot when the phone was allowed to swing on a pendulum oscillating left-right, with a screen of the phone facing the user.


how do I interpret that graph?  I sort of understand the data points at ~0.83Hz - the amplitude gets smaller, the period stays the same - but what are the other data points?  

Also, the results screen on that very experiment read that the period/frequency is 1.19s/0.84Hz (the same is shown on the Autocorrelation results screen).  Shouldn't it be expected that the values on period/frequency match those on the autocorrelation (and they do) and on the Resonance results?

Finally, in the case of a practical pendulum, where due to practical limitations both the amplitude and the period change over time - is the frequency provided in the results the average frequency over the experiment time? If not - what is the logic used to give that frequency value?

thank you for creating such a useful application!

[Jens Noriʇzsɔɥ]

The graph is for forced oscillation in order to record the pendulum response (amplitude) like in the video to the spring oscillator www.youtube.com/watch?v=VbL4IInVAO4, for instance.

The result tab shows the latest value provided by the autocorrelation. The algorithm is documented in the experiment info via three-vertical-dots menu – or the .phyphox source, of course…

[jmnk]

The graph is for forced oscillation in order to record the pendulum response (amplitude) like in the video to the spring oscillator www.youtube.com/watch?v=VbL4IInVAO4, for instance.

The result tab shows the latest value provided by the autocorrelation. The algorithm is documented in the experiment info via three-vertical-dots menu – or the .phyphox source, of course…

Thank you so much for a prompt response.  I'm sort of a physics enthusiast only so it is entirely likely I do not properly understand the experiment.  I get the meaning of that 'resonance' graph for the driven pendulum case - I just wonder what it means for a non-driven case.  

For a practical pendulum, non-driven, the amplitude gets smaller with time (due to damping), and the period of oscillation does get smaller with time as well (I suppose due to various friction/imperfection of a practical experiment?).  Both the change of amplitude and the change of period gets smaller with time.  Since 'resonance' graph plots normalized amplitude vs frequency one would expect that the resulting graph would show a decreasing amplitude as frequency increases - which my graph does indeed do that somewhat.  But I do not understand why there is clump of data points at ~0.83Hz and another at ~0.8357Hz.  What is so special about those particular frequencies?

[Jens Noriʇzsɔɥ]

I just wonder what it means for a non-driven case.

Not so much… ¯\_(ツ)_/¯

But I do not understand why there is clump of data points at ~0.83Hz and another at ~0.8357Hz.  What is so special about those particular frequencies?

Uneducated guess: perhaps some “quantization” in the numerical autocorrelation algorithm? I need to check that…

[jmnk]

I just wonder what it means for a non-driven case.

Not so much… ¯\_(ツ)_/¯

But I do not understand why there is clump of data points at ~0.83Hz and another at ~0.8357Hz.  What is so special about those particular frequencies?

Uneducated guess: perhaps some “quantization” in the numerical autocorrelation algorithm? I need to check that…

Thank you.  If you have a moment to check that - that would be great. I'm trying to read the the .phyphox source to see what the logic is - but it will be few days before I fully understand.   

[solid]

Dear JMNK,

in order to understand physics of oscillations try to use "Acceleration spectrum" from "Tools" choosing the number of samples 4096 (for the best frequency resolution). Normally there is an amortization of the oscillations which gives some (constant) increase of the period and corresponding width of the (single) resonance peak. Unfortunately I do not have "acceleration without g" on my smartphone and I cannot  check the phyphox programs you are using.

Mikhail

[solid]

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.

       

[Jens Noriʇzsɔɥ]

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)…

[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?

---

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.

[solid]

Jmnk, you have to open this forum on your smartphone and click the program. Then choose 'open in phyphox' and save the program in your collection. The editor does not support colors.