An LC circuit has L = 4.0 mH and C = 9.0 μF. The capacitor is initially charged to 12 V. Find (a) the oscillation frequency, (b) the maximum current, (c) the energy oscillating in the circuit. Step 1: ω₀ = 1/√(LC) = 1/√(4.0×10⁻³ × 9.0×10⁻⁶) = 1/√(3.6×10⁻⁸) = 1/(1.897×10⁻⁴) ≈ 5270 rad/s. f₀ = ω₀/2π ≈ 839 Hz. Step 2: Initial charge Q₀ = CV₀ = 9.0×10⁻⁶ × 12 = 1.08×10⁻⁴ C. Maximum current I₀ = ω₀Q₀ = 5270 × 1.08×10⁻⁴ ≈ 0.569 A. (Equivalently, energy conservation: ½LI₀² = ½CV₀² gives I₀ = V₀√(C/L) = 12√(9/4 × 10⁻³) ≈ 0.57 A ✓.) Step 3: Total energy U = ½CV₀² = 0.5 × 9.0×10⁻⁶ × 144 = 6.48×10⁻⁴ J ≈ 0.65 mJ. This fixed packet of energy endlessly converts between electric (capacitor) and magnetic (inductor) forms, a quarter-cycle apart.