The article deals with linear homogeneous stationary systems of second-order differential equations with the property of exponential stability. The hypothesis is verified that the value of the overshoot of such systems can be calculated as the ratio of the maximum and minimum eigenvalues of the Lyapunov matrix. This hypothesis can be used for research in many areas of applied mathematics and control processes. To test the hypothesis, the overshoot value was calculated for systems of a certain type, the calculation method of which may be applicable for a wider class of systems. On the basis of concrete examples, it is shown that this hypothesis is not fulfilled for all systems, and therefore this task requires further study.