Physics
Resonance
Driven oscillations: amplitude and phase response, Q factor.
What happens
A damped oscillator pushed by a periodic force: drive it slowly and it follows meekly, drive it fast and it barely moves, but near its natural frequency the amplitude blows up into the resonance peak drawn on the A(ω) curve. Lower the damping and the peak grows taller and narrower: that is the Q factor. The bob's displacement is visually compressed. The charts retain the model's actual displacement.
Equations used in the module
Equations x'' + 2βx' + ω₀²x = F cos φ; φ' = ω(t) A(ω) = F/√((ω₀²−ω²)² + (2βω)²) φ_lag = atan2(2βω, ω₀²−ω²); Q = ω₀/(2β) β < ω₀/√2: ω_r = √(ω₀²−2β²)
