Given a sinusoid input of frequency f, an RLC network, no matter how complex, should produce a sinusoidal output of frequency f, with possible attenuation and phase shift. At least that's my understanding of AC circuit theory, and confirmed here. It follows from the fact that, at a given frequency, any R, L, or C can be viewed as a complex impedance following the complex version of Ohm's law, E=IZ.
Yet, even these simple LC circuits change frequency, or produce beat frequencies:
Even if we assume that the components have parasitic resistance, capacitance, or inductance, they still should form a passive linear RLC network.
How is it possible to explain the behavior shown? And, more importantly, if I can't use the classic AC circuit theory of complex impedances to analyze them, how do I analyze them? And how do I know that the classic AC circuit analysis will not apply here?