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Question: Is a general RC circuit, with any topology of interconnected R and C elements, never underdamped?

This is a bonus question in one of my homeworks. The answers to the earlier questions in the problem indeed show that two example RC circuits are not underdamped.

I understand how one identifies over-damped, critically damped and under-damped for a small circuit, using the Laplace transform on the differential equation. But for any general RC network, I do not know how to write the equations.

I attempted a proof by induction, but dint get far.

Thanks for the help!!!