[AstralStorm]

That is way too simplistic as well, as this model is time invariant. Most instruments, due to physical nature of excitation, are variable in both frequencies and phases over time.

It is the main reason why modelling physically is the best way for realistic results right now - lossy lumped finite element models typically - digital waveguides are one of such models.

In such a model you can incorporate nonlinear damping and resonance functions over time at desired accuracy.