Sure you can, you only need to simulate it to near some orders around the planck constant. And then you can go even further. Analog does not have infinite precision either
But due to limitations of physics, nothing will be continuous.
Is amount of water in a bucket continuous? No, you can count each individual atoms. So you can simulate that by using large enough integers. Same principle applies everwhere
These are assumptions. If you think the assumption of continuity is ridiculous, note that the definition of universal Turing machines requires an infinitely long tape (infinite memory), which of course conflicts with the finite memory of any actually implementable digital computer.
I am not saying you need a turing machine, a finite one will do since we are also dealing with a finite analog system. If analog system is finite and has finite states that we can measure, then a finite computer will just do fine
> A digital computer cannot emulate an analog computer: it can only simulate it to an arbitrary level of precision. That’s the whole point.
A modern digital computer can simulate this particular analog computer beyond the noise floor. Practically speaking, that means a digital computer can perfectly emulate this system therefore it's simply a toy or perhaps for aesthetics.