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In the paper are determined some mechanical properties of some types of the mechanical systems that have certain identical parts. It can be noted that similar problems occur frequently in engineering practice, many mechanical systems used in these areas exhibiting symmetry properties resulting from the design process, fabrication reasons, simplicity, cost or logistics. In the paper we determine the properties of the eigenvalues and the eigenmodes of transverse vibrations in a mechanical system with continuous system of bars. The determination of these properties allows the calculus effort and the computation time and thus increases the accuracy of the results in such matters.