Analog Explorations: Simple Gravity (publ. 2025-02-11)

My progress toward improving my breadboard analog computer has been delayed by lack of funds. There is a bucket list of parts I want to purchase from mouser, in particular the somewhat expensive multipliers ($20 USD/ea), some solid state relays, and a few other components required for building comparators. After paying the last set of rent and utility bills, there is no comfortable margin for buying electronic parts. But I'm hoping to place an order after the next paycheck comes in.

Of course, I still have the modules I've already built. Trying to understand more about modeling differential equations, I sketched out this simple model:

diagram for simple gravity module (falling object)

The "g" symbol is the gravity constant, controlled by a potentiometer, and we start with the velocity IC tied to +15V, i.e., the object has been shot up into the air. In this screenshot, green is the velocity, and yellow is the vertical position.

scope screenshot with +15V initial velocity

Some things I learned:

(1) For accuracy in calculations, it is not practical to have separate mechanical switches, one for each integrator. Is it difficult to get them both switched at the exact same time, and any difference in start time makes a lot of difference in the calculation result, even at slow calculation speeds. So I plan to replace those with solid state relays tied to one switch.

(2) The integrator for velocity showed significant non-linearity outside of the +/- 5V range. I can do the calculations within that range, if I want, but then the noise from my noisy workbench area is a lot more pronounced on the screenshot:

scope screenshot with +5V initial velocity

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