Mechanical systems, proper oscilations, and spectral theory of selfadjoint operators

In the paper on some examples we illustrate the following thesis. In all cases it is possible to reduce the problem of of finding proper oscillations of a holonomic nondisspative mechanical system to the problem of obtaining eigenvalues and eigen elements of the corresponding selfadjoint operator in the Hilbert space. The scalar product in the space is determined by the quadratic form of the kinetic energy. Bibliography: 1 title.