Re: [Phys-L] Trinity Pendulum Q

[Bernard Cleyet <bernardcleyet@redshift.com>]

On 2015, May 25, , at 19:45, brian whatcott <betwys1@sbcglobal.net> wrote:

> Donald,
> I spent some time pondering the various determinations for the Trinity clock recovery exponential. I can get an expression for the exponential fit of the October 2009 recovery which is reasonably close to Bernard's, but different from your fit for the March 2009 recovery.
>
> Here are some factors which may be relevant:
> 1) The March 2009 decay was a modest one millirad before the drive was reengaged - just 2% in fact. The October 2009 data had a usable 10 mrad decay range and a usable 11 mrad recovery range 

I found veerry diff. time constants for the decay-recovery.  

> 2) Your  fit forced an amplitude of an equivalent decay by manipulating the data and by using a distant final amplitude value - where it is known that the amplitude varies somewhat with time.
> 3) You were using 300 second averages for this recovery. I suppose that the Trinity averaging scheme is an arithmetic mean of one hundred readings for each value, so that is not an ideal basis for exponential curve fitting.

OK with much more data?

IIRC, (a COA) I used the max. i.e. 3 seconds, the minimum averaging.  I suspect the photogate measures the beat and then averages it.   Perhaps because the detector is not at BDC.  I have my detector on a stage with resolution < (better than) 50 micron.  And, curiously, BDC changes w/ amplitude.  

> 4)Your model fit was given as R^2 = 0.8997
> Both Bernard's and my fits to the wider ranging October 2009 data gave R^2 values better than 0.999, probably because the equation used for fitting also allowed the  final amplitude to be fitted - using either
> Amplitude = A*exp(-B.t) + C or   (me)
> Amplitude = A(1-expt(-B.t)) +C    (Bernard)  

This is similar to the thread on forcing a fit thru zero, no?   Final A is unknown, IIRC.

> Either result being comparable to the other by manipulation of parameters A and C
>
> Sincerely
>
> Brian W


bc