Yes, it is complex or it appears to be, and especially the manual gives you here not a lot of that interaction: case in point here the number of springs. What springs are used if the number is small? The only reasonable answer I can up with is, the springs close to the moving joint, and the more springs involved the more the effect shows. Well, I might be wrong here, and if I’m, then certainly based on the need to interpret the manual than getting a more detailed instruction here.
So, lets lower the complexity.
https://www.amazon.com/clouddrive/share/XNah3dfO_sAyxeflLjeFfHEmDHQIO3hk9eGj4Bc-Y28?ref_=cd_share_link_copy
Have a look how each step influences the areas of the cylinder itself, how fast it gets back (and oscillates or stopped) and how far it moves).
OK, testing the thesis, with many joints along a Cylinder. The more springs are involved the more detailed the effect is, from 1 to 4 springs for example. So, if you found a good number, leave it there. (To make things more visible, crank up the Motion Scale for the time being.)
Now change another value, the Iteration. Higher numbers will speed up the process, and if you miss details then they are hidden based on the fps (e.g., Nyquist Frequency), but it moves along the initial impulse and its consequences—just faster.
To get the change, and I know you wrote about the springs that you don’t like to go there. But lets put it into a nut-shell for now. Stiffness and Structure and the two springs. Stiffness stands for the ease how it can be influenced and how fast it goes back to the initial state. The Structure is more a parameter how far the change goes. (I stick all the time to the cylinder deformed first by joints)
I have several backgrounds, many degrees, e.g., in fine art as well in science, so I understand your idea how it should look like (I hope at least I do), but I also know that ignoring parts of the equation leads to the feeling that the subject must be complex (leaving out the springs or changing them with other stuff at the same time). I strongly encourage to build the cylinder with many joints and change always ONLY ONE parameter. If you change two or more, the results are useless, except you got what you want accidentally.
I have attached the little set up, I’m certain you have no problems to set this up on your own, but just for communications sake.
On the other hand, and I have said it often here in the past decade, any automatic or kind of dynamic procedural, has the complexity you mentioned. Based on that, it is not always the best way to get the expression you as an artists are after. Yes, it is more work to set it up otherwise (e.g., PoseMorph) but that separated the average from great artists, to go that extra mile, if comfortable options show limitations. If you are in full control, the results are always closer to the vision you had about your scene.
My best wises