Vibrations of buildings and structures, transport and construction equipment, various mechanical engineering and instrument making objects are of undoubted interest. Analytical methods are in most cases ineffective. The finite difference method and other numerical methods for calculating elastic elements with simple geometry are very relevant and attractive. Numerical methods are distinguished by the simplicity and transparency of algorithms and computer programs [1–3]. The formulation of the initial-boundary value problem on the dynamic loading of an elastic rod is presented [4–6]. With its hinged ends, the spectrum of eigenvalues (frequencies) and functions (shapes) of vibrations is determined, which are used in problems of vibrations under the action of an external harmonic load. The vertical stand is compressed by an axial force under its own weight or the weight of the equipment. The d'Alembert principle is used. In problems about eigenvalues and functions, boundary conditions are added to the equation. The upper end of the rack is free, and the lower end is rigidly fixed. Eigenvalues cannot be found in closed form.