For nondestructive testing (NDT) and nondestructive evaluation (NDE), the low‐frequency vibroacoustical free‐oscillation method is used. For the first time, a theoretical investigation is carried out to differentiate between spectral density and decrement of free oscillations of testing objects in the presence and the absence of fatigue cracks taking into account the internal friction in the object material. The new analytical dependencies of the spectral density and decrement of testing object‐free oscillations from the relative crack size, factor of internal friction, duration of NDT(E), and initial object speed are received, on the basis of which the new multidimensional vector of testing data for NDT(E) is proposed. Experimental results with aircraft engine blades in the presence and the absence of fatigue cracks, which match with theoretical results, are presented. The received results are common; therefore, they have been found to be expedient in taking into account the obtained results for forced oscillation NDT(E) methods.