Comment by JKCalhoun

Just playing with it a bit, the default setup (a decaying value/voltage)…

Lower left, "-1/+1" are your source voltages representing the smallest allowable value (-1) and largest (+1).

Upper left "COEFF" are the coefficient multipliers—potentiometers, that take a voltage/value in (circle) and output (triangle) an attenuated value/voltage. You change the potentiometer values with the "COEFFICIENT POTENTIOMETERS" section on the right side of the split view.

The top section of the analog computer represent the all-important "INTEGRATORS" (5 of them). Circles are inputs (a few 1x and 10x each) and the output are the triangles.

A lime green wire connects from the +1 source voltage to the #1 coefficient multiplier, that attenuated voltage/value feeds "IC" on the first integrator. ("IC" represents the initial condition of the integrator—the value/voltage it defaults to when the machine is reset.)

That first integrator's output (triangle) is being fed into a second coefficient multiplier where the output from that is fed back into the input of said integrator. In short, the integrator is feeding back a portion of its output back into itself.

Another wire (purple) from that integrator goes first to an inverter in the "INVERTER" section (probably obvious what this operator does) and then connects to the "X" of the "OUTPUT" section. The oscilloscope is displaying "X" on "CH1" (channel 1). We see the decaying voltage/value of the integrator on the oscilloscope.

Playing with the coefficient multiplier sliders: P2 represents the amount of feedback, thus the speed with which it decays. If you turn on "AUTO-RUN ON EDITS" you can watch the oscilloscope change after moving a slider.

(Please let me know if I got something wrong above.)

EDIT: created a "hello world", mass+spring for the simulator—you can download the JSON file [1] and try uploading it to the simulator: in the "Design File" section you select the JSON file and "LOAD FILE"—set "OP-TIME" (underneath the oscilloscope display) to 100 ms or so and then "RUN".

You ought to see the position trace of a damped mass on a spring. Coefficient multiplier P1 determines spring constant, P2: damping, and P3 the mass of the spring.

Challenge: see if you can modify the demo to also plot the velocity of the mass+spring (integrator #1) on the oscilloscope (hint: use the "Y" output).

[1] https://drive.google.com/file/d/16d0MLmc9Tk8SSlqz8RtLDBxXeAz...)