Modal Spring Reverb based on Discretisation of the Thin Helical Spring Model

The distributed nature of coupling in helical springs presents specific challenges in obtaining efficient computational structures for accurate spring reverb simulation. For direct simulation approaches, such as finite-difference methods, this is typically manifested in significant numerical dispersion within the hearing range. Building on a recent study of a simpler spring model, this paper presents an alternative discretisation approach that employs higher-order spatial approximations and applies centred stencils at the boundaries to address the underlying linear-system eigenvalue problem. Temporal discretisation is then applied to the resultant uncoupled mode system, rendering an efficient and flexible modal reverb structure. Through dispersion analysis it is shown that numerical dispersion errors can be kept extremely small across the hearing range for a relatively low number of system nodes. Analysis of an impulse response simulated using model parameters calculated from a measured spring geometry confirms that the model captures an enhanced set of spring characteristics.