Modeling of both death wobble and oscillatory trailer sway requires the use of differential equations. People spend their entire lives studying this stuff. And I have seen models that involve as many as 20+ variables for trailer sway. Hence why there never is a single answer on how to cure either problem.
Have you ever hit a bump in your Jeep but had the steering wheel shimmy and return to rest? That steering shimmy is an example of an underdamped system, that allows the shimmy, but eventually returns the system to stability.
If you hit the bump and develop full blown death wobble, then that is an example of a negatively damped system. Even though there was only one single input, the system resonates and the energy builds into a very violent oscillatory action.
If you hit the bump and your steering wheel jerks to the side and eventually returns, that is an overdamped system. That is the preferred operating mode if bump steer is unavoidable.
Trailer-car systems are exactly the same way. Consider the following system:
You are pulling a trailer with your Jeep at a constant speed on a flat highway. A semi flys by you and the wind pushes the trailer sideways.
In the ideal case, the system is overdamped, and you simply correct the path of your Jeep and trailer by changing the position of the steering wheel. This typically occurs at low speeds.
In the less than ideal case, the system is underdamped. In this case, the trailer sways back and forth, and the operator keeps the Jeep pointed straight. Eventually the trailer sway fades away on its own. This typically occurs at higher speeds, near the critical speed.
In the worst case, the system is negatively damped. In this case, the trailer sway begins from the impulse of the blast of wind, but then grows so large you get exactly what happened in the video. This occurs when the driver has exceeded the critical speed. The only hope the driver has is to use the trailer brake controller to engage the trailer brakes and induce tension on the coupler. If he or she does not do this or doesn’t have a brake controller, the oscillation grows until the vehicle jacknifes, leaves the road, or flips.
If the driver happens to be doing exactly the critical speed, the trailer would oscillate at the same intensity forever until the driver alters the system by slowing down or braking the trailer.
All the methods of reducing trailer sway have the effect of increasing the critical speed. On a really poorly set up system, trailer speed could be as low as 45 mph. On a really well set up system, it could be 150 mph+. On most on-road combinations it is usually between 70-120 mph. U Haul imposes a limit of 55 mph on all their trailers because they assume the average renter is too stupid to set it up correctly.
Divergent (non-oscillatory) trailer/steering action such as jackknifing or bump steer can be reduced to conventional math, and are easier to study.