I'm reading through Hayt's Engineering Circuit Analysis 9e and it does a fairly good job of giving the intuition for "where" the energy is going in a damped RLC circuit, but I'm hoping that someone here can help me get full closure.
Consider a parallel RLC circuit with no input and where the capacitor is initially at some non-zero i(0).
First of all, I'm hoping to clarify why the maximum voltage achieved by the system occurs in the underdamped case. Intuitively, is this because the resistor's value value is so large that most of the current will flow between the capacitor and the inductor (and thus energy is just exchanged between the two rather than being dissipated by the resistor).
If the above is true, then I am trying to square that with the fact that the slightly underdamped or critically damped case has the shortest settling time. My understanding is that settling time corresponds to the time required for all of the energy to be dissipated. If, in the slightly underdamped case, we are exchanging energy between the capacitor and the inductor in an oscillatory manner and the resistor is therefore not dissipating much energy, how does that system settle (well) before the overdamped case where the resistor (I think) dissipates a large amount of energy because resistance is low and much current therefore flows through the resistor? Or am I somehow confusing energy dissipation with the voltage here.
Generally, I'm looking for an intuitive explanation of "where the energy is going" and why it "goes away" quickest in the critically damped or slightly underdamped cases, rather than a mathematical demonstration.