I read your article and word document. But I was not able to build a physics model for your case.
Because I do not fully unstand the whole situation.
I tried to search google with keyword "physics of archery", but I can not find similar situation.
To build a simulation we need a model.
I need to find equations for all the forces/torque in the system.
You also have some "forced vibration" , may I know the form of the force or the amplitude and direction of the vibration.
"The restoring force for the rotatory component of the motion is a vector component of the bows draw-force that acts to pull the bow in line with the line of force. "
But what is the magnitude of the force when it is pointing at different angle (deviate from the line of foce)?
Does the so called "line of force" is a fixed vector or is it going to be changed with time?
I am not familar with archery. I need physics model to generate simulation. Please provide me with detail information or we need to discuss ,and make some assumptions, to build a complete model to simulate it.