LC Tank Circuits and Resonance
An LC circuit — an inductor and capacitor connected together — naturally oscillates at a specific resonant frequency, exchanging energy back and forth between the inductor's magnetic field and the capacitor's electric field. At resonance, the circuit's reactance is minimized (or maximized, depending on configuration), which is exactly why LC circuits are used to select or reject a specific frequency in radio and RF applications.
The resonant frequency formula, f = 1/(2pisqrt(L*C)), shows an inverse square-root relationship: doubling either the inductance or capacitance doesn't halve the frequency, it divides it by the square root of 2 — a common source of miscalculation when designing a filter or oscillator by hand and expecting a simpler linear relationship.
Real LC tank circuits underpin radio tuners (selecting one station's frequency out of the full spectrum), bandpass/notch filters, and oscillator circuits where a stable, specific frequency is the entire point of the design.