Really a rope bridge only has three primary behaviors.
First it sags SOMEWHAT beneath a load at the point of contact.
Second it sways laterally when a load is applied.
Third it bobs up when a load is removed, which can result in a vertical oscillation as well.
So bottom line create a system that handles these in a manner that looks good and be done with it. None of these three behaviors should be difficult or should require complicated physics applications. After all a bridge sags in an arch shape which I''m sure you could find a simple enough function to model...how about the cosine function? Then treat the entire structure like a simple rope attached at both ends. Whichever section attaches to the plank that is stepped on will be pushed down...as you go out on either side push them down less according to a function (again just figure something out that looks nice). When it is removed make it pop back up, but maybe introduce a harmonic oscillation in there. As for the lateral sway, that''s just a lateral wave.
So the SECOND bottom line (
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) is this: Pretend like your bridge is a plain old rope. Then introduce vertical deformation and possible waves due to a load, and lateral waves due to a load. Make it look good and use physics if you want, but if you get into something much more complicated than sine and cosine functions you''re probably making it too complicated.