Dynamics of a mechanical system consisting of two identical pendulums with the same length and weight is investigated in the present paper. Its supposed pendulums are connected with linear spring which length in the undeformed state is equal to the distance between points of the suspension. All trivial and non-trivial states of equilibria have been obtained, and their stability has been studied. Analysis of the systems dynamics on one-dimension manifold for which angles of the declination have the same values and opposite signs is presented. The results are presented in the form of bifurcation diagrams.