Comment by pierrec
Having done a fair amount of audio physical modeling, I'll just say a synthesized version that's both fast and realistic would be possible but difficult. The difficulty is at least "it would make an impressive presentation at DAFx [1]", though I might be underestimating it, and it's more "you could make it your master's thesis at CCRMA [2]"
Ideal springs are a common, simple element in this field, but this kind of spring is very much not that.
You're probably better off improving the sample-based version by fading out the audio when necessary and using different samples based on the way it's triggered. If you have "ultra-dry" samples (maybe taken with a contact mic), you can add a convolution effect with a well-chosen impulse response, this will allow you to sharply cut off or adjust the audio and still have a natural-sounding tail.
I'm extremely grateful for this. My most deeply held secret is that I wish I could do this for a living - digitally modeling weird/beautiful objects/instruments and work on that forever haha. (And maybe make pedals out of them, I don't know)
If you don't mind humoring me (I'm quite the novice in this field), if I automated the recording of "all" possible positions for a spring (say I had a motor positioned in a way that would let me pull the spring in any polar direction), would that make modeling potentially easier?
There might be a "train an AI, here's 1000 recordings" angle, but I'm not necessarily interested in/asking about that.
Just strictly for modeling, would it help the R&D phase to have a lot of high sample rate recordings? Thanks a lot!
P.S. Also, if you have a good intro to DSP class/book, I'd love to hear it. I know about a few, but a recc is always appreciated