🔌 LC Oscillator — Energy Sloshing Between L and C

It applies fourth-order Runge-Kutta (RK4) integration to the pair of first-order equations q' = I and I' = -(R·I + q/C)/L, taking 8 smaller sub-steps every animation frame so the update stays numerically stable even at the extreme ends of the L, C, and R sliders.

R models real wire and coil losses that convert electrical energy into heat. In the RK4 update, the current's rate of change includes a term -R·I/L that opposes the motion, so each swing of charge and current loses a little energy; push R high enough and the circuit becomes overdamped, decaying to zero instead of ringing.

They visualise conventional current flowing around the loop. Their direction flips with the sign of the current I, and their speed is drawn proportional to |I| relative to the slider-dependent scale maxI = q₀/√(LC), so a faster stream of dots means a larger instantaneous current.

It illustrates the exact analogy behind the code: the charge q is mapped directly onto the spring's displacement, because both obey the same differential equation (m·x'' + k·x = 0 versus L·q'' + q/C = 0). Watching the spring stretch and compress in step with the capacitor's charge shows that the electrical and mechanical oscillators are solving identical maths.

They show the instantaneous split of stored energy between the capacitor's electric field, E_C = q²/(2C), and the inductor's magnetic field, E_L = L·I²/2. As the simulation runs the bars trade height: E_C peaks when the capacitor is fully charged and current is zero, E_L peaks a quarter-cycle later when current is maximum and charge is zero, and in the lossless case (R=0) their sum stays constant.