Mesh and Nodal Analysis - Source Frequency

[JJBladester]

Homework Statement

Mesh and nodal analysis are used to find unknown currents and voltages in planar networks. Why is it necessary when performing these network analyses that all of the source frequencies be the same?

The attempt at a solution

I know that superposition let's us analyze multi-source networks whose sources have different frequencies. I read somewhere that "for sources having different frequencies, the total response must be obtained by adding individual responses in time domain."

The math behind mesh, nodal, and superposition analysis all seems to be phasor algebra with numbers being either complex or polar in format. Also, we're not working with f(x)=Asin(omega*t+phase) in any of the analysis techniques. We're working with amplitude/phase (phasor) notation.

Somebody in my class posted the following, but I am not sure how it factors into the fact that mesh/nodal cannot be used for networks with sources of different frequencies:

"Well, if we have different frequencies in the circuit sources, the only method we can use to solve is Superposition. This is because the effects of the individual sources can be analyzed by themselves in the frequency domain. Nodal and mesh analysis require us to solve in the frequency domain and convert the results to the time domain if necessary."
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[gneill]

The network will "look different" at different frequencies since the impedances of the reactive components depend upon frequency. Thus you cannot, for example, assign a single frequency to a mesh current and single values to impedances for your KVL "walks".

Note that there's nothing stopping you from using mesh and nodal analysis one source at a time and using superposition to combine the results.