ẍ + 2ζω₀ẋ + ω₀²x = F₀cos(ωt). Linear textbook resonance: amplitude peaks near ω = ω₀√(1−2ζ²) and the analytic curve A(ω) = F₀/√((ω₀²−ω²)² + (2ζω₀ω)²) is overlaid.