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This looks like a cool project in the same spirit!
That idea was shamelessly inspired by the soft fluidic robot some years back.
The way you usually run an analog computer is to put it into fast repeat mode (which they call REPF), where it cycles between initial condition mode and run mode. Outputs go to a scope. Then you can twiddle the knobs and see the output respond immediately.
The other modes are used mostly during setup and debug.
Hours of fun. Ages 14 and up.
[1] https://www.alibaba.com/product-detail/YIXINTAI-DSO138-Digit...
One of the hardest 10 weeks of my life, but also one of the most rewarding. Our team was one of the few that actually got it working in the end. I had to custom-make a gigantic breadboard to hold the entire circuit.
Today I still work in hardware, but mostly with digital circuits. While my analog knowledge has decayed over the last decade, that project and it's success gives me great confidence any time I have to deal with the domain.
If you want to take a look, here's a pretty similar project: https://www.analogmuseum.org/english/examples/bouncing_ball_...