Remember when I said "you know nothing"? This is precisely why. What I have not seen mentioned is what happens to tire inflation pressures at different temperatures and how that affects the spring rate of the tire. I have also not seen any mention of the resonant frequency change in the front suspension as the weight transfer happens going up or down hills.
When I say "you know nothing", it also means I know nothing. The more I learn about DW, the less I am convinced I know.
For every single point, there is an equally valid counterpoint which refutes the point making both null and void.
I was just going to mention the relation between frequency, stiffness and mass...
The specific relation is:
Critical Frequency = sqrt(stiffness/mass)...(sorry I can't use proper engineering notation here)
While the mass may not vary while driving a specific vehicle, (well, you could have mud accumulated, or throw a wheel weight), the mass can and does vary from vehicle to vehicle, and with variations in wheels and tires.
And while it is true that the critical frequency is dependent on the mass of the moving component, the moving componet (axle, wheels, tires, steering linkage) is all tied to the vehicle...the mass of which varies from vehicle to vehicle (think hard top/soft top, winch, passengers, engine, etc).
Now, let's look at the stiffness term. As you pointed out, variations are present with respect to tire pressure, loaded or unloaded suspension, tire stiffness (sidewall height, number of belts, tire design).
But wait, there is the variations in stiffness of the control arms, their bushings, the all important track bar, ball joints...even the knuckles themselves.
With all these variables, some of which are non repeatable, it's no wonder that DW (under damped or unstable, or inadequate log decrement, in my world) is so difficult to predict.
If I had the time, I would like to take FFT measurements of the axle motions with an accelerometer, from a wide range of vehicles, with their various tire sizes, lift springs, worn bushings, etc.
Maybe then, a near universal solution can be created.
From my professional perspective, all of this DW discussion is fascinating.
As a Jeep owner who had DW at 70 mph, I also find this terrifying...
And finally, one more point and I'll stop blathering:
A wise man knows what he'll never know,
A fool knows everything.