# Re: Frequency splitting...... Food For Thought

```Original poster: Jared E Dwarshuis <jdwarshui@xxxxxxxxx>

We can actually use a mechanical model of a tuned coupled oscillator
to gain insight into the nature of the phenomena of "Frequency
Splitting"

We can have a spring stuck to a wall with a spring constant k and a
mass m . Then we add a coupling spring (k prime) then an identical
mass followed by another duplicate spring k (which we attach to the

Now we need a relevant starting point. Let us hold the left mass
stationary at its natural resting point where displacement equals
zero.

Let us now displace the right mass an arbitrary unit of 1 to the right
of its natural resting point.

Now let us examine the predicted frequency of the left mass at the
instant where time equals zero.  It is simply:  w = sqrt (k/m). But
what is the instantaneous frequency at time equals zero of the right
side's mass that is displaced one unit.
It is:   w = sqrt(( k plus Kprime)/m)

Now the interesting part,  is that given a duration of time we will
find that the mass on the left has been displaced by -1 unit, and the
mass on the right will have zero displacement. Thus at this instant in
time, they have switched frequencies, where the right side now has the
left sides old frequency, and the left side now has the right sides
old frequency.

Implication: The frequency for a given side is constantly changing
between sqrt (k/m) and the sqrt of ( k plus k prime)/ m.

```
Sincerely: Jared Dwarshuis
```
```