Frequency splitting (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Sun, 19 Aug 2007 15:22:28 -0400
From: Jared Dwarshuis <jdwarshuis@xxxxxxxxx>
To: Pupman <tesla@xxxxxxxxxx>
Subject: Frequency splitting

                                                    Frequency splitting



If we build a circuit with two identical parallel LC oscillators that have
been coupled with a third capacitor ( which we will label as C') we can
easily describe the beat frequency as being comprised of two individual
frequencies: w+ = 1/sqrt(LC) and w- = 1/sqrt( L( C + 2(C') )



We can make remarks about the charge amplitude and show the beat frequency
as being comprised of w+ and w-



q = 2 q0 sin [ ( w+ +  w-  )/2   t ] cos [ (w+  - w- )/2   t  ]



We can also model a pair of identical mass /spring's  coupled with a central
spring labeled k'  by using the exact same mathematical underpinnings.



In this case w+ = sqrt (k/m) and w- = sqrt [(k + 2k')/m]



Wall-----Spring k---Mass--- Spring k' ----Mass--- Spring k -----Wall



We can make remarks about the amplitude and show the beat frequency as being
comprised of w+ and w-



x = 2 x0 sin [ ( w+ +  w-  )/2   t ] cos [ (w+  - w- )/2   t  ]



Now to give some physicality. We find the two fundamental modes of this
coupled mass spring system by examining two special cases of motion.



When we move both mass the same direction and distance, we find that the
central spring k' remains flaccid and does not contribute to the frequency
of the system. In this case the term k' disappears and we get w = sqrt (k/m)



When we move both mass in opposite directions and equal distance. We are
stretching the center spring k'. This is where we get the second frequency:
w- = sqrt( (k + 2k') /m)



Now if we were to introduce dampening to one side of our mass spring system
we could no longer make these simple remarks. We would need to write all of
this using decaying exponential functions.



But in a pinch we could always get a lightly dampened system to respond
decently to the driver by tweaking one or more of: m, k, or  k'



Now does it makes sense to use the phrase "frequency splitting". Not really
since it is already implied that we have a superposition of two frequencies
in a coupled system. The beat envelope increases as we diminish k'. this is
no surprise since:

 w- = sqrt( (k + 2k') /m) becomes: w = sqrt (k/m) as k' goes to zero.

 End.



Commentaries:



It has come to my attention that many experts on Pupman are now describing
the plasma arc from the secondary capacitor  as having a capacitance. They
are tuning coils as if the capacitance was really there.



There is no such capacitance in the arc. Capacitors do not increase
capacitance when they arc out. Arcs do not have an ability to store charge.
Arcs  do not have plates nor can they be described with a fixed geometry.



Nor can we describe an arc as having an appreciable inductance. The geometry
is not much good for inductance.



Nope!;  you are altering C or C'  to make up for changes in frequency caused
by dampening. (dampening from  the non linear resistance of the arc)



Empirical corrections are wonderful, my hats off!  I am sure that a great
deal of effort was involved in arriving at a useable correction factor. But
there is no capacitance in the arc. There is only non linear resistance and
perhaps a tiny bit of inductance.





Jared Dwarshuis  August 07