Abstract
Gladwell [Gladwell GML. Minimal mass solutions to inverse eigenvalue problems. Inverse Probl. 2006;22:539-551] found an explicit solution for the inverse eigenvalue problem of an in-line system of masses and springs with one given spectrum corresponding to the fixed-free end conditions, and a minimal mass condition. In this paper we formulate and solve a continuous counterpart of this problem; i.e. we construct a continuous rod for a given free-fixed spectrum and a minimal mass condition. This reconstruction is based on the analysis derived by Gopinath and Sodhi [Gopinath B, Sondhi MM. Determination of the shape of the human vocal tract from acoustical measurements. Bell Sys. Tech. J. 1970;293:1195-1214] by which the cross sectional area of the rod can be reconstructed from the impulse response.
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