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The temperature dependence of the frequencies of a Bose-Einstein condensateobtained in experiment has not been fully understood theoretically. In thispaper we present a simplified version of a two-gas model. A numerically-foundground state of the system is used for the small-oscillations analysis. In thecase of spherical symmetry a full spectrum of frequencies is found for loworbital quantum numbers. Avoided crossings that appear in the spectrum might bethe reason for experimentally observed frequency shifts.Comment: 11 pages, 10 eps figures included in the manuscript, submitted to  Journal of Physics

Finite temperature oscillations of a Bose-Einstein condensate in a two-gas model