Re: [Phys-L] Timing Statistic

[John Denker <jsd@av8n.com>]

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.