A mathematical model of construction of the total mechanical energy of a discrete statically loaded dissipative system in the process of free oscillations in the form the time analysis method, which is based on the study of the characteristic quadratic matrix equation, was given. The features of the behavior of the parameters of the dynamic response when the elastic structurally nonlinear system to a new state was shown. It is also given the expressions to determine the kinematic (displacements, velocities, accelerations) and force (restoring, dissipative and inertial forces) parameters of the dynamic response. The criteria for assessing the load bearing capacity of the structure at the non-linear operation was suggested. Using a mathematical model is illustrated by the example of the calculation of flat steel statically indeterminate roof truss during the process of free oscillations, which was caused by a sudden failure of one of the bearing elements. Turning off the rod caused by the loss of strength as a result of chemical cracking due to corrosion effect.