The inverse problem for the vibrating beam

The beam is modelled by a system of rigid rods joined together by rotational springs and with masses at the joints. The left end is clamped while the right end is subject to one of a number of conditions: it is free, pinned, sliding or clamped. It is shown that the resonant and antiresonant frequencies of the system may be almost completely ordered. Necessary and sufficient conditions are found that these frequencies must satisfy to correspond to an actual system, with positive parameters, and two stripping procedures are devised for the determination of these system parameters, from a knowledge of certain frequency spectra.