2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/22369The 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.RevTeX4, 10 pages, 6 figuresMaterials Sciencetext