Resonance- Circuit and Mechanical

*StandardBasis*

I am studying the analogy between mechanical oscillations and AC circuits.

For a mass on a spring, resonance occurs when there is a phase difference of 90 degrees. It seems like for a series RLC circuit, resonance must occur at a phase different of 0 degrees between the voltage from the source and the current (because inductive and capacitive reactances cancel).

Why does the analogy break down there?

Simon Bridge

For mass on a spring - where is the driving force applied?
Compare with how the driving force is applied in a RCL circuit.

AlephZero

If you look at the differential equations for mechanical and electrical oscillations, the analogy is that displacement corresponds to charge, not to current.

Current corresponds to velocity in the mechanical system, not to displacement. That's where the "90 degrees difference" comes from.

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Simon Bridge Recognitions: Homework Help	For mass on a spring - where is the driving force applied? Compare with how the driving force is applied in a RCL circuit.

AlephZero $Math 2012$ Recognitions: Science Advisor	If you look at the differential equations for mechanical and electrical oscillations, the analogy is that displacement corresponds to charge, not to current. Current corresponds to velocity in the mechanical system, not to displacement. That's where the "90 degrees difference" comes from.