Abstract: A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question:How many types of the periodic small oscillation ill the whole configuration space of the system are there? Making some hypotheses, it expresses the lower bounds of the number of the types for two cases where critical points of the potential function are nondegenerate and degenerate respectively by tile Betti numbers and dimension of the constraint manifold only.

Key words: large-scale estimate, periodic motion, Morse theory