Re: [Phys-L] Trinity Pendulum Q (was Re: checking the work for minus signs ... et cetera)

["Donald Polvani" <dgpolvani@verizon.net>]

I did an exponential fit to the March 29, 2009 Trinity clock data.  I selected data from t = 600 s to 10,500 s after start-up where the plotted curve was smooth and rising.  I used the data points supplied every 300 s.  I translated all times by 600 s, so that my t' = t - 600 s.  I translated amplitudes by the amplitude at t = 600 s (i.e. theta(t')' = theta(t) - theta(600), so that at t' = 0, theta(t')' = 0.  I then formed the difference y = theta_0' - theta(t')'  where theta_0' is the translated amplitude evaluated at very large t'.  I used the value theta_0' = theta (10500) - theta(600) = 0.968892 mrad as evaluated directly from the Trinity data.

In Excel, I did an exponential fit to the function:  y = theta_0'*exp (-gamma*t').  Because of my definition of y, this gives an exponentially falling curve from theta_0' (at t' = 0) to 0 (at very large t').  I got from the fit:

gamma_fit = 5 x 10-4 rad/s
theta_0_fit' = 0.9874 mrad

Using Q = omega/(2*gamma_fit), yields, for omega = 2*pi/T = 2.09 rad/s for T = 3s, Q = 2100.

I checked the above fit by evaluating the equation for y at a single point (t' = 2400s, theta_0' = 0.968892 mrad, y = theta_0' - theta'(2400)  = 0.257527 mrad), solved for gamma and got gamma_check = 5.52 x 10-4 rad/s in reasonable agreement with the Excel fit given that the check was done at a single point and Excel used all the points.

Don

Dr. Donald G. Polvani
Adjunct Faculty, Physics, Retired
Anne Arundel Community College
Arnold, MD 21012

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of Bernard Cleyet
Sent: Monday, May 18, 2015 2:37 PM
To: Hugh.Hunt
Cc: Douglas Drumheller; Phys-L@Phys-L.org; Bryan Mumford; hemh@eng.cam.ac.uk; Bob Holmstrom; Tom Van Baak
Subject: Re: [Phys-L] Trinity Pendulum Q (was Re: checking the work for minus signs ... et cetera)

All!

Here’s my fit to the restart:  



Only every 30th datum is plotted.  

If my hypot. is correct, my questimate’s running Q is v.~ 1k, this method, which, of course, disagrees w/ the known drive method.

I presume the decay preceding the above is completely free, so I’ll “bc” analyze it.

bc required too long to know he could download every datum instead of 1/300th, and is too lazy to cheque Lupton’s thesis for the PG flag width.  

On 2015, May 17, , at 23:10, Hugh.Hunt <hemh1@cam.ac.uk> wrote:

> Dear Brian,
> I'm glad we agree!
> You might find this interesting to ponder:
> In 2009, October clock change, rather than putting it back one hour it was advanced by 23 hours. This meant that the free decay of the pendulum was even slower, because the gravity arms were lifted off the pendulum. But the interesting question is the restart. The exponential curve that shows the swing amplitude getting back to normal surely tells us something about the drive?
>
> <http://trin-hosts.trin.cam.ac.uk/clock/?menu_option=​data&from=​25/10/2009&channel=​amp&channel2=​0&to=​25/10/2009&xmax=​2&skip=​0&ymax=​54&ymin=​37>
>
> Food for thought.
>
> Best wishes
>
> Hugh
>  
>  
>  


cut (much)
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