In the article, the equation of the equivalent movement of the oscillator with viscous friction is provided. The statistical specifications and the spectral approach for the density of intensity of the established vibrations are provided. Non-stationary vibrations in the closed form are investigated. The statistical characteristic for intensity of vibrations is obtained. The work presents a method of investigation of vibration processes of random mechanical vibrations in the equipment and apparatus. The vibratory system of a sufficiently small (as compared to vibrations of a long wave) size is described; the models with the limited number of degrees of freedom are applied. The statistical theory for discussing of vibrations at constructional damping is applied.