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. The period T = 2π √((m/k)) depends only on mass and spring constant, not gravity, which affects pendulums but not spring systems. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result The restoring force is independent of gravity follows, reflecting SHM dependence on amplitude A, ω and system parameters.