You wouldn't really need an incremental force: a step-function force (first backward for some time steps, then instantly forward) will still produce a continuous velocity curve.
true! I suppose you'd risk getting some oscillations in the anticipation depending on the scale of the force, but that could be desirable, or might not happen if the scale is small enough, and certainly makes the math a little easier
You can trivially calculate the time-to-peak overshoot using the closed form equation. It’s the first (0-indexed) zero of the velocity response, i.e. happens at t = (pi / scale)
And obviously it would only apply for the underdamped case.
