This sort of reminds me of when we discussed dynamic systems in EE16B -- especially when talking about stable and unstable systems. The setup was very similar, where to get the next state, we use the previous state and add a transform, but in that class we used matrices to show how we transition from one state to another. This meant that if you wanted to see if a system was stable, it was straightforward -- just find the eigenvalues of the matrix and see if they are < 1. I'm curious if there is something similar or analogous here?
@nikhilJain17 Great observation! Yes this is analogous, you could perform the same analysis with these systems.
This method is not an accurate representation of the transitions because it assumes that the force applied to a particle over the time is consistent. In reality, the force applied over the time changes because of other springs moving and the results of those movements propogating to other springs.