Re: [Phys-l] question on averaging.

[John Denker <jsd@av8n.com>]

On 02/18/2009 10:21 PM, Bernard Cleyet wrote:
> I'm analyzing the free decay of a pendulum à la Siegel [AJP 76 (10)  
> 956.]
>
> However, the pendulum has such a large Q (few hundred => ~2k) that I  
> must average over several data points.  Since the necessary values  
> are the speed squared there are two orders.  One to average the  
> squared speeds and tother to square the averaged.  The difference is  
> not large as over most of the decay the loss is rather small. [Which  
> is why I must average!]  Also the factor of interest is the  
> difference between the squared points (speeds).  So the question,  
> which is the correct  order, if there is one?
>
> bc  thinks this is more a meta-physics question

Metaphysics is not required.  Physics suffices.

 -- Energy is (strictly) conserved.  Speed is not.
 -- Energy is almost constant from cycle to cycle in this system.
  Speed is not.
 -- Q is conveniently defined in terms of energy.
 -- KE goes like speed squared (at corresponding points in
  the cycle).

Therefore, unless there are special additional requirements, as-yet
unmentioned, speed squared (or, better, energy) is the way to go.
A big part of physics consists of connecting experiment to theory,
and in this system the connection is easiest in terms of energy.

Also note that "averaging" is a lame substitute for curve-fitting.