Re: [Phys-l] What comes first, the equation or the explanation?

[Bernard Cleyet <bernardcleyet@redshift.com>]

On 2011, Dec 23, , at 18:58, Bob Sciamanda wrote:

> For what it’s worth, here are two casual observations:
> 1) If one does the experiment of changing the mass, he must simultaneously 
> change the driving frequency, since the resonant frequency is mass 
> dependent.

Very good --I hadn't seen that, and so obvious!.  I think one may check this by changing the mass in such a way that the omega sub zero stays the same (i.e. in the simple case L is the same)  Then driving it.  Is the resonant frequency now different, as predicted.   Not incidentally, this may be a clue as to why the amplitude decreases.

Furthermore, this effect, evidently, has never been reported by horologists.



> 2) It may be worth noting from equation 4 that if “omega sub zero” is used 
> as the “resonant” driving frequency, then the amplitude B is independent of 
> mass.


But that's not the resonant frequency!   The resonant frequency, supposedly, is found by differentiating WRT the amplitude and setting equal to zero.   Several texts do this without giving the trick in differentiating.

bc thanks Bob S.

p.s.   All this is complicated by how to drive a pendulum harmonically, especially w/o adding complications, e.g. additional dissipations.   The easy method is to use a clock drive, but then it's impulse, and no method of driving doesn't add dissipation.   Also as is obvious from the result eq. 6a (or 6 for those more adept than I at "interpreting" the equation.), the effect is minuscule unless the Q is low and the mass (initially) low.