In this paper we discuss the stability and instability properties of two classes of conservative dynamical systems which are comprised of a finite dimensional and an infinite dimensional subsystem. The finite dimensional component is a linear mechanical system with gyroscopic terms. The mechanical system is coupled to a wave equation defined on an infinite spatial domain via two different types of coupling which we denote by Lamb coupling and wave field coupling. We also investigate the effect of dispersion on the coupled system. In particular, we analyze the conditions under which coupling to a wave system induces instability in the finite dimensional system. Analytic results are compared to computer simulations.