Practice question

**Driven system** exhibits amplitude-frequency response peaking at resonance, phase shift between drive and displacement varying 0° to 180° across resonance. Forced oscillations sustain motion against damping, amplitude controlled by detuning |ω_d - ω₀| and damping strength b. Velocity: v = ω A cos (ω t + Φ) . A = 4 m, ω = 3 s⁻¹, Φ = -(π/3) . At t = (π/6) : 3 × (π/6) - (π/3) = (π/2) - (π/3) = (π/6) . v = 3 × 4 cos (π/6) = 12 × (√(3)/2) = 6√(3) ≈ 10.39 m/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt