The precision, vibration devices using dependence of acceleration of moving object from frequency of fluctuations are considered. Analyzed devices have the small geometrical sizes, high frequency of fluctuations, small admissions on functional characteristics. For the solution of a task the device of mathematical physics is used in the analysis of fluctuations of a beam variable (generally) sections taking into account internal friction at various types of boundary conditions. The settlement circuitry of the instrument, having two channels and using the differential frequency of fluctuations of channels taking into account certain admissions is developed. The developed model considers properties of a material (internal friction), on the geometrical sizes, a deviation of a form of section from nominal rate and influence of these parameters on functional characteristics – dependence of acceleration of the device on a difference of frequencies of fluctuations of channels of the device in a certain interval of temperatures allows to consider admissions.