Abstract: Consider a simply connected grounding springmass system, it is supposed that j mass is connected to the ground. Let (λ,X) and (μ,Y) be two eigenpairs of a simply connected grounding springmass system. The inverse eigenvalue problem of constructing the physical elements of the system from (λ,X),(μ,Y) and j mass was studied. This problem was transferred into an inverse eigenvalue problem for Jacobi matrices. The necessary and sufficient conditions for the construction of a physical realizable system with positive mass and stiffness elements were established. If these conditions were satisfied, the grounding spring-mass system can be uniquely constructed.

Key words: spring-mass system , eigenpair, inverse problem