  The spectrum of acoustic vibrational modes of an inhomogeneous elastic
continuum are analyzed with application to a spherical nanoparticle embedded in
an infinite glass block. The relationship of these modes to the discrete
vibrational spectrum of a free sphere is studied. The vibrational modes of a
sphere with a fixed surface are relevant in some situations. Comparisons are
also made to calculations of mode frequency and damping based on complex valued
frequency.
