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This seems restricted to just an oscillating system. Neural ODEs (DiffEqFlux) seem a bit more general than this to learn any kind of dynamical system

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As an example application, it would be cool to have a vehicle know when its shocks need to be replaced or if they are too far out of specification, just from monitoring suspension arms' angle sensor/s.

Yo, your car's shocks need replacing. It is currently underdamped and going to bounce around like a Ford Fiesta in an LA earthquake.

Hey buddy, those pricey tuner shocks are problematically over-damped which will lead to a rough ride, wear issues, and handling problems.

I don't understand why you need "machine learning" for that. The engineers already have fea models which they build reduced order dynamic equations out of. By monitoring the response, you can estimate the damping factor relatively easily which could provide the feedback whether your shocks need to be replaced.

I mean some people take machine learning to include anything with parameter fitting, but it seems like classic engineering to me.

Yeah you just need an accelerometer and you can find out if your damper is broken with an FFT. OEMs are just very price sensitive so only the expensive vehicles will get this, even if it's a cheap component.

Analyzing data collected over time to see how shocks degrade .

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