The problem of resonance oscillations of inertial inclusions in contact with elastic waveguides has triggered a number of theoretical investigations. It was shown [1-3] that related phenomena may be treated by solving the spectral problem posed for a differential equation that is defined in an infinitely long interval. For specific waveguide and inclusion parameters, a composite system that includes interacting objects with lumped and distributed parameters may have a mixed (continuous and line) eigenfrequency spectrum. The line spectrum may be observed both before and after the boundary frequency. It was noted [3, 4] that the presence of an isolated lumped inertial element causes the line eigenfrequency spectrum, which extends to the boundary frequency. So-called trap oscillations are responsible for this spectrum. However, little is yet known about these effects, which hinders their effective use in practice. First, conditions for trap oscillations should be generalized for the case of multielement inclusions in various infinite waveguides. Second, the effect of edge conditions on the line spectrum in a semi-infinite waveguide calls for in-depth investigation. The solution to these problems would formulate proper ways of tackling engineering challenges associated with the interaction of a railway track with high-speed rolling stock [5]. Issues discussed in this paper are also concerned with object characterization from analysis of its eigenfrequency spectrum. In recent years, this technique has gained wide acceptance in crystallography and other fields of science and technology as a promising tool for the acquisition and processing of data on the internal structure of an object.