Drop and Listen

Drop and Listen: a ball bouncing on a damped oscillator

Each mode: m_p(q_p'' + 2σ_pq_p' + ω_p²q_p) = −f_c; ball: m₂u₂'' = −m₂g + f_c; contact f_c = k_cδ^3/2(1 + λδ') while δ = Σq_p − u₂ > 0. The sound is the contact point Σq_p. Pick a method and a sample rate, press Drop, and compare with Reference. More info: [the model]

target: f₁ = 400 Hz drop = 15 cm sample rate: method:

Animation

Target motion ×1000.

Bounces and ringing, 2 s

Color: simulation. Gray: reference (RK4 at 16 × 44.1 kHz).

Spectrum of the sound

Gray lines: exact mode frequencies. Gray curve: reference. Color: simulation.