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Could one build a mechanical equivalent to electric circuits ?

I'm considering mechanical waves (like shock waves) travelling through a medium here. I'm aware that due to the high loss and practical constrains it is not something that would have an immediate use, but it seems quite logical that using different material densities etc, one should be able to build the equivalent of resistances and derive some equivalent of Ohm's law. But could we do equivalents of capacitors and coils ? Surely this has been researched before (I guess).

Could we then modulate a shockwave in frequence and amplitude? Has this ever been used before, or does it have known applications ?

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There is already a very useful mechanical equivalent called the hydraulic analogy. You'll find lots of related posts already on this site.

All analogies have their limits, but the hydraulic analogy is remarkably good. You can even represent components like capacitors, inductors and even semiconductor junctions.

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As you may know, You can equate a damper with a capacitor and a spring with an inductor.

You'd need to transfer the energy from your wave somehow to those mechanics in order to use the damper and the spring.

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