Inverse Eigenvalue Problem for a Class of Spring-Mass Systems

Abstract

This paper discusses the constructional problem for a class of spring-mass systems whose part particles are connected to the ground. The problem is converted to an inverse eigenvalue problem for Jacobi matrix. An inverse eigenvalue problem of determining the system from its some physical parameters and incomplete eigenpairs is solved. The necessary and sufficient condition for constructing the system uniquely with positive parameters is obtained. Furthermore, the concrete expressions of the solution and the related numerical algorithm are derived, and numerical results show that the algorithm is effective.