The main concept of LC filters depends on the impedance equations for the source, load and Z of each reactance. Computing just as any other 2 element tap from a true 0 ohm voltage source.
Here , There is one frequency when the impedance of the Inductor is the exact opposite of the capacitor, both conducting voltage out of phase +90 deg , -90deg yet sharing the same current. When this happens with identical magnitude impedance in series (between 0 Ohms of the theoretical Voltage source and 0 Ohms of a theoretical ground,) both elements create a perfect 0 Ohm short circuit with no reactance ( as they cancel) with an infinite current loop and infinite voltage at the midpoint ( or output here).
In practice since there is always some wire and ground and component DC resistance or DCR in the magnet wire and ESR in the capacitor electrode interface, the current is never infinite, meaning the Q is never infinite as the gain of voltage ratio to source at this 1 very precise frequency. Practical Q of 100 is possible but difficult to control. Q of 1000 is extremely difficult if not impossible for most.
But it is useful to make oscillations grow for oscillators or a combination low pass + resonant bandpass filter. The only way to dampen this Q is to apply a load resistance and if that ratio equals 1 you get a damping factor which still has ringing and does not become critically damped with no overshoot until the resistance is equal to 0.707.
At this point the resonant frequency is shifted slightly due the impedance damping effect of R so that R and C share the same current from L so that when L and C impedances are equal, the voltage rise is damped by the R load and so the voltage overshoot can be minimized or eliminated depending on the impedance ratios of R to X at resonance for either L or C. This is important for passive crossover speakers.
However RF filters use LC components and often complex filters with many many LC components can be computed for a maximally flat frequency response or linear phase shift or even for data for ringing at the data period regardless of 1T, 2T, 3T/2 frequencies ( Raised Cosine Filters).
for example a Chebychev maximally flat filter has much high Q’s than 1 but with shifted poles or resonant points make the bumps equally spaced and as small as possible (0.1 dB or 3dB) with the advantage of the higher Q skirt bandstop.
Not all inductors of the same value are identical since every component be it a cap or resistor or inductor or wire or air has some measurable capacitance, resistance and inductance even if beyond your measurement skills. The are called parasitics, because a wire lead or trace is an inductor 0.5~1 nH/mm roughly, and air or FR4 between close pads and tracks can be a capacitor at some pF/cm depending on geometric ratios of conductors. So when it comes down to high currents or wide bandwidth , these real parameters come into effect.