In the analogy of pushing the child, the length of the swing determines the resonant frequency. In that case, is the LC (length*capacitance?) circuit the equivalent of swing length?
Also, with pushing a child, I don’t need to push every cycle, I can push every other cycle (1:2), every third/4th cycle (1:3,1:4), or 2 out of 3 (2:3), etc.
Is there an equivalent with radio? Can the LC circuit be tuned to half the signal frequency and still pick up?
The swing length, to first order, is independent of the period, as Galileo noticed while watching a swinging lantern during a church service. He timed it with his pulse. It's the period (or its inverse, frequency) which is characteristic of a resonance, not amplitude.
Interestingly, the period of the resonance is proportional to the geometric mean of the capacitance and the inductance. The proportional factor is 2pi, which is there because of the "rationalized MKS" units chosen. (If it wasn't for that, one Farad resonating with one Henry would have a period of one second.)
You're quite right: pushing every other cycle is analogous to pulsing an LC in phase every other cycle. This is done using a class C amplifier[0], which puts out short pulses at the input frequency. The parallel LC in the amplifier load resonant at twice the input frequency sees in phase current pulses in its inductor every other cycle, which add energy. That's how a frequency doubler works, and the technique works for higher harmonics, also, as you thought.
> LC circuit be tuned to half the signal frequency
In the case of a swing, that would work, because the child isn't there for half the pushes. But in the case of an LC tank, the "pushes" always inject current into the coil in the same direction, so half if them will be out of phase and cancel the previous one.
Sorry, by “swing length” I meant the length of the rope of the swing, not how far it swings (amplitude). You’d agree that Galileo saw lanterns on longer ropes swing slower?
> In the case of a swing, that would work, because the child isn't there for half the pushes. But in the case of an LC tank, the "pushes" always inject current into the coil in the same direction, so half if them will be out of phase and cancel the previous one.
Thank you for clarifying that for me! So, no “AC” antennas?
Also, with pushing a child, I don’t need to push every cycle, I can push every other cycle (1:2), every third/4th cycle (1:3,1:4), or 2 out of 3 (2:3), etc.
Is there an equivalent with radio? Can the LC circuit be tuned to half the signal frequency and still pick up?