Normalized Wave Digital Mass-Spring Oscillator

• Stored energy invariant with respect to time varying and/or nonlinear changes in mass or spring constants
• For the piano hammer, the felt spring constant may vary with force $f_k(n)$ without altering stored energy
• Only the reflection coefficient $\rho(n)$ varies as the spring is compressed
• Note delay-free interdependence of $\rho(n)$ and $f_k(n)$
• See Bensa & Bilbao et al. (SMAC-03) for an update on the lossy normalized wave digital piano hammer