06-14-2020, 04:59 PM
(This post was last modified: 06-14-2020, 05:03 PM by Jens Noriʇzsɔɥ.)
Excellent timing: we have just discussed such a pendulum a few days ago when analysing students' setups for the “pendulum” experiment. 
However, we have not really pursued the math. As far as I know, this is Ackley's ballistic pendulum. Are you aware of references that go beyond the energy conservation part? If the length of the linkage is (and stays) identical, it should perhaps behave like a simple gravity pendulum even for unequal mass distribution thanks to all the constraints…
The width of the FFT “signal” appears to be rather wide that might be an issue here. The algorithm for the autocorrelation graph of the “pendulum” experiment should work better: take the distance between the first two maxima (in the debug tab) as an estimate, set windows for the next maxima, and determine the right most maximum. Then divide the elapsed time by the multiplicity of it.
Taking the zeroes would be more precise – possibly going beyond the capabilities of phyphox' analysis tool.
p.s. the second FFT “signal” could be attributed to the damping?
However, we have not really pursued the math. As far as I know, this is Ackley's ballistic pendulum. Are you aware of references that go beyond the energy conservation part? If the length of the linkage is (and stays) identical, it should perhaps behave like a simple gravity pendulum even for unequal mass distribution thanks to all the constraints…
The width of the FFT “signal” appears to be rather wide that might be an issue here. The algorithm for the autocorrelation graph of the “pendulum” experiment should work better: take the distance between the first two maxima (in the debug tab) as an estimate, set windows for the next maxima, and determine the right most maximum. Then divide the elapsed time by the multiplicity of it.
Taking the zeroes would be more precise – possibly going beyond the capabilities of phyphox' analysis tool.
p.s. the second FFT “signal” could be attributed to the damping?