# Mass,Spring, Damper vs Capacitor, Indcutor, Resistor vs ? analogy

## Main Question or Discussion Point

From a mathematic, linear differential equation point of view, and energy storage point of view, the concepts I mentioned in the topics are the same (I remember this being a concept in modeling control systems.)

My question is, what are the same basic elements in other topics: thermal principes (I've heard of thermal resistance, is there thermal inductance?), hydraulics, etc?

-Matt

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Claude Bile
These concepts are analogous because the equation that governs the interaction between the said quantities is exactly the same (namely the wave-equation).

Any additional analogies would have to obey the wave equation and thus have to exhibit some kind of wave-like behaviour, which is why I have my doubts there exists an appropriate thermal analogy. You could get an electromagnetic analogy using permittivity and permeability or an acoustic analogy using density and bulk modulus though.

Claude.

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While I am not familiar with the details, I know there are thermal circuit models used in real applications. In particular, the analyzer made by these people: http://www.klippel.de/ uses a circuit model for the thermal behavior of a loudspeaker.

Also, I don't see why these analogies have to obey the wave equation? Circuit models are another way of expressing constant coefficient differential equations, not just wave equations.

Claude Bile
Can you define a thermal frequency? Can you define a thermal phase? Can you obtain a thermal resonance? These are the doubts I have as to whether one could obtain a perfect thermal analogy.
Nolen Ryba said:
Also, I don't see why these analogies have to obey the wave equation? Circuit models are another way of expressing constant coefficient differential equations, not just wave equations.
You could feasibly come up with a similar analogy that obeys a higher order differential equation, or even a nonlinear differential equation if one so wishes. The point was that all the parts of the analogy obey the same basic equation (even if all the terms represent completely different things). That's what makes an analogy so.

Claude.

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