Equations describing the behavior of plasma oscillations that can arise on the surface as well as inside metallic spherical nanoparticles are obtained in the random-phase approximation. The frequencies of all characteristic plasma oscillations arising on the surface and in the volume of a particle are determined. It is shown that the volume plasma oscillations can give rise to forced oscillations on the surface of a nanoparticle. The effect of plasma oscillations on the optical properties of a dielectric medium containing metallic nanoparticles is determined.
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