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Re: [Phys-L] Timing Statistic



John,

Sorry for the incautious use of the term variance. You are correct, and I
will try to be more careful.

Here's the raw data with a model that replicates the position data using a
multiple linear regression with both t and t^2 terms.
https://drive.google.com/open?id=1oHf0zcq3Q_yWS7452ETSrXdVXfCWLM8p
The model reliably predicts the position of the disk within 0.03 radians
for most of the sample data.

I took a set with the device recording at 100 samples per second and
another at 20 samples per second.

This model doesn't seem to predict the velocity well. Feel free to
critique that model. Or suggest that the sensor is reporting something
other than the real angular velocity. (It's doing a weighted line fit to
the slope of the position data. This is evident from the way the first and
last data points for velocity are clearly incorrect.)

From the residual plot on the velocity its clear that small numbers of
points have a standard deviation of about 0.05 radians/s.
This may be due to a real physical wobble in the disk.

Thoughts?
Paul



On Thu, Nov 8, 2018 at 3:54 PM John Denker via Phys-l <
phys-l@mail.phys-l.org> wrote:

On 11/8/18 10:00 AM, Paul Nord wrote:
Experiment results...
https://drive.google.com/open?id=1HXxHjf4sZQchVtPEOW0hYDmZsbl5Vzwx

Ah, data.

Data moves the discussion forward.

I've got a motor connected to the rotary motion sensor to drive it at a
constant speed. Here is the variance as a function of the number of
samples collected over a 10 second interval.

Minor point:
Please do not say "variance" when you mean standard deviation
or vice versa. The graph says standard deviation; the email
(above) says variance.
-- Standard deviation is σ.
-- Variance is σ^2.

I'm suspicious that the motor was still warming up during the first trial
and slowly changing speed. The later trials were some minutes later.

There's a lot to be suspicious about here.

What are we learning from this?

There's something nasty going on.

The motor-driven data is not conclusive. It's pretty clear
that "some" major nastiness is due to the motor, but it's
not clear whether that is the whole story.

Suggestion #1: Spin the disk up to some goodly initial
velocity (via motor or otherwise) and then let it spin
down slowly, due to friction alone. This removes the
nastiness of the motor from consideration. The velocity
will not be constant, but it will be a /simple/ function
of time, which we can easily model.

Suggestion #2: Rather than tracking just the standard
deviation, record the raw data.
a) If angular velocity is available as a function of time,
that's good.
b) If angular position is available as a function of time,
that's even better.

Rationale:
*) From either (a) or (b), it is straightforward to calculate
anything else. (In contrast, working backward from the
standard deviation is not at all straightforward.)

*) We don't know what Vernier might be doing to cook the
data. Therefore we want to get our hands on the most raw,
most upstream, most unadulterated data.
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