Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] data manipulation -- analysis



Also: Important: If the photogate data is unduly noisy, maybe
you shouldn't be using a photogate!


The photogate:

http://www.bmumford.com/mset/access/access.html

the interface:

http://www.bmumford.com/mset/model3.html


I'm again a victim of my "telegraphy".

The data is noisy, because the "physics" is. The pendulum is subject to random dissipation, e.g. air turbulence, variations in the escapement friction, etc. while the primary dissipation is rather small, i.e. the Q is hundreds. So the KE(n) - KE(n+1) is small while the KE is large. Thus w/o smoothing one obtains negative Qs, and sometimes 10^(+/- 38).

Averaging 10^38s doesn't work (tho I haven't tried). So I smooth several times usually n +/- 3, 5, and sometimes as much as 21on the way to the Q.

Fitting Q is only appropriate for portions of the decay, because it's a mixture of quadratic, linear, and da Vinci dissipation.

Another similar analysis without this limitation:

http://www.cleyet.org/Pendula,%20Horological%20and%20Otherwise/Period-speed%20perndulum%20siegelAJP000956.pdf


Generally: Q for da Vinci (Amontons-Coulomb) dissipation is proportional to the amplitude, linear is independent, and I've been unable to analytically derive or find Q for quadratic dissipation. However, the amplitude decay is: a/(1+b*t), which is initially similar to linear's exponential decay. Those fits to decay result similarly, so it is difficult to separate them in the case of clock pendulua.

The (cleyet) quasi continuous Q method: 2Pi*E/(delta E) = 2Pi* (1/t^2)/(delta (1/t^2), Where t is the photogate interrupted (blocked) time.

http://www.cleyet.org/Pendula,%20Horological%20and%20Otherwise/HSN/HSN%20published%20articles/PDFs/*%20*Q%20from%20t%20@%20BDC%20(submitted%20v.).pdf


Here are some graphs showing the problem:


http://www.cleyet.org/Pendula,%20Horological%20and%20Otherwise/noise%20problem/



On 2012, Apr 06, , at 13:28, John Denker wrote:

On 04/06/2012 10:28 AM, Bernard Cleyet wrote:
interrupt time data from a photogate by a clock pendulum is very
noisy. In order to analyze and display (graph), it's necessary to
"smooth" it (Kaleidograph's word for average). It's intuitive that
one should square then average instead of the reverse order.
Otherwise there is a cross product,** no? Also it's convenient first
to smooth the speed data. Should one smooth the raw (interrupted
time) data before inverting, or invert and then smooth? The two do
not result in the same value. Of course the difference is very
small, as the difference between successive data is very small
(otherwise any noise would not be obvious!).

You need to reformulate the approach.

You have a data reduction problem. In simple cases, this can
be formulated in terms of /curve fitting/.


response above


To say the same thing the other way: If you formulate it in
terms of "smoothing" you have already lost the game before it
begins.


Really?

The basic steps include:
a) figure out what variables are directly observable

The max. (or relative) KE as inferred from the blocked time of a photogate. (small angle approximation: amplitude proportional to the speed at BDC, KE prop. to the speed squared.

b) figure out what variables describe the physics you are
most interested in.

The variation in the KE


c) figure out the relationship between the observable
variables and the interesting variables. Typically this
takes the form of a parameterized model, where the parameters
are the "interesting" variables.
d) come up with a model for the noise.

More accurately: the initial motivation: to find the effect of Q on the noise -- roughly qualitatively the RMS error to a linear fit of the pendulum's period and amplitude with varying Q (added sail). Pic. here:

http://www.cleyet.org/Pendula,%20Horological%20and%20Otherwise/noise%20problem/IMG_0656AR.jpg


e) fit the model to the data.

============

Also: Important: If the photogate data is unduly noisy, maybe
you shouldn't be using a photogate!

If I were doing this, I wouldn't use a photogate. I might use
some sort of gray-coded position sensor, as we have discussed
before. There are lots of other possibilities.
_________________________________

Using a mouse is a possibility, but would not solve the noise prob. and would swamp me w/ data.

http://physics.mercer.edu/hpage/mouse-sensor.html

I have used a Rotary Motion Sensor, but it's not a clock suspension and its da Vinci dissipation, except with massive bobs, results in low Qs.

http://www.cleyet.org/Pendula,%20Horological%20and%20Otherwise/HSN/HSN%20published%20articles/PDFs/Corrected%202%20Oscillating%20Pendulum%20Support.pdf

bc

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l