Overdamped-Wave Historical Modeling

While I doubt that many here have taken classes in vibrations, controls, or second-order differential equations, most everybody understands the simple shock absorber and what happens when they go bad.

In wave theory, a wave is said to be critically damped when an oscillating mass, say a car, reaches the stable state again at the shortest period of time. That is, the amount of opposing damping force is just enough to prevent the thing from going past neutral and 'bouncing,' and not too much which has the effect of slowing the response down to a crawl. Thus, a new shock absorber is relatively closer to that critically damped state, while a worn one could be described as underdamped. An underdamped vibration shoots past neutral stability because the reaction was too strong for the damping force to control, while an overdamped vibration has too little reaction force and too much control.

Apply wave theory to any historical topic you'd like. Just about all of politics can be modeled by some wave form or another. Some trend is shown, and a reaction to that trend quickly arises, which pulls the trend in the opposite direction. While there are those forceful zealots that would like to return back to where they see the center to be, invariably the result of their over-reaction is to swing the pendulum of the debate the other way, and further delay a return to normality, essentially an underdamped vibration. And when governments are too tied up in beaurocracy to react to the initial trend, an overdamped result occurs, and again, normality is delayed.

Now the trick is that both the damping force and the spring force can be changed mid-stream by the addition of a new factor. Take the birth of the church as a prime example. To certain groups of Jewish and Christian zealots, the showy religious pride of the ruling bodies was reprehensible hipocrasy in action. And with Christ himself railing against such behavior in recorded word, the scene was set for extreme piety and humility to be the official party line for the rest of time, even if it proved too hard to follow in actuality, especially for the ruling class. I picture this trend as a vibration that initially went undamped, swinging too far into the proud side of equilibrium, and then swinging violently towards the hyper-humility of the early church apostles and later monks, but then was restricted by the overdamping effect of biblical canonization, which effectively froze the damping constant at a high value, with the church wanting to avoid swinging back towards the boundary. In fact, you might say that with the conservative evangelical movement, that the pendulum is being racheted back towards the pious end. Just imagine what would happen if the church were to influence that pendulum even more, essentially pegging it. But then the church were to suddenly fall apart, the rapture would happen, etc. Suddenly, the damping force nearly disappears altogether, and the now free-swinging pendulum ride gets wilder. Add a little more force, and now you have an unstable environement.

Is this why the sine wave is abreviated 'sin?'