• $summary_{type}$: concept
• $word_{count}$: 150

A charged capacitor connected to an inductor creates LC oscillations at omega = 1/sqrt(LC). The energy shuttles between electric (Q^$\frac{2}{2C}$) and magnetic ($LI^2$/2) forms, with total energy constant: Q^$\frac{2}{2C}$ + $LI^2$/2 = $Q_0$^$\frac{2}{2C}$. This is mathematically identical to a spring-mass system: L corresponds to mass m, 1/C to spring constant k, Q to displacement x, and I to velocity v. When Q = $Q_0$ (maximum charge), I = 0. When Q = 0, I = $I_0$ = $\frac{Q_0}{sqrt(LC}$) (maximum current). The oscillation period T = 2pisqrt(LC). In practice, resistance causes damped oscillations — energy is gradually lost to heat. A driven LC circuit with small R shows resonance when the driving frequency matches the natural frequency 1/sqrt(LC). This is the principle behind radio tuning circuits.