As a mathematician* your description really appeals to me. It is the mechanical example of the Intermediate Value Theorem...
https://en.wikipedia.org/wiki/Interm..._value_theorem
from which this quote...
"In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f (a) and f (b) at some point within the interval."
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* OK, I'm not really a mathematician. My degrees all say 'physics' on them but, when you study physics, you automatically get deeply involved with mathematics. I enjoy math and have continued learning about it long after leaving school.
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