I don't think I understand the point you are making. Power = product of two quantities. You have these two quantities in various domains: I and V, F and v, T an

I don't think I understand the point you are making. Power = product of two quantities. You have these two quantities in various domains: I and V, F and v, T and O, P and Q, ... The analogizing comes from saying "I is like P and V is like Q", or vice versa. 2nd order ODEs are very common, and I agree that it is unifying to see different systems modeled by the same equation. But I think more fundamental than that is the understanding of "through" and "across" variables, the notion of a "port" [1], and series/parallel toplogies for combining two one-port components to form a new one-port component. You could still make an analogy between domains, even if you don't have second-order ODEs. This is clear even from your comment because, note that a spring+damper is going to be a first-order ODE. You would need moving mass to store kinetic energy, in addition to the spring to store potential energy. [1] https://en.wikipedia.org/wiki/Port_(circuit_theory) https://en.wikipedia.org/wiki/Port_(circuit_theory)