Re: [Phys-l] Q from amplitude width?

[Bernard Cleyet <bernardcleyet@redshift.com>]

On 2011, Apr 25, , at 01:03, John Denker wrote:

> Additional advice, pertaining to this particular equation of motion:
> There are several different definitions of Q in the literature.
> They are all equivalent in the high-Q limit, but may differ when
> Q is small.  This is discussed in the Feynman lectures somewhere.
> So pick one definition, stick to it, and explicitly communicate it 
> to all concerned.
> ___

True the two I use are equivalent for linear dissipation w/ Q > 50  [~ < a few percent difference.] **

My question was how to extract from the data*** of the response the Q defined by the narrowness of the response in order to compare w/ the exponential free decay definition.   

> The usual answer to all such questions -- a verrry wide range of questions --
> is to parameterize the equation of motion and then curve-fit the data to
> extract the parameters.


This is how I find the Q from the free decay.

I now see how I can do that for my experiment by varying the drive (gamma) to keep B constant in the equation:

B = (Gamma / mgL)   * C1 / sqrt[ (c1-1/c1)^2   + 1/Q^2],  where C1 = resonant (natural) frequency / drive frequency, B is the response amplitude , and Gamma is the drive amplitude.

But I'm maths challenged.   



** My source for most of my work is Baker and Blackburn, "The Pendulum".
***i.e. where on the graph is the 0.707 (or half power) reduction.

bc now thinks he has a method to proportionally compare, but not absolutely from the graphs.