In this paper, the free vibration analysis of a double-beam system is investigated. This structure is formed by two beams with elastic restraints at one end and free at the other end. These beams are connected by a mass-spring device. First, the related eigenvalue problem is established in the frequency domain, employing the well-known Fourier transform. Then, by utilizing eight boundary and compatibility conditions and solving two differential equations, the eigenvalues of the system are found and tabulated for different amounts of the parameters. Furthermore, some mode shapes of the mechanical system under study are plotted for various values of the springs’ stiffness. In order to verify the results, some special cases are analyzed, and their outcomes are compared with the available ones.

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