Abstract—The harmonic balance (HB) principle is a powerful and convenient tool for finding periodic solutions in nonlinear systems. In the present paper, this principle is extended to transient processes in systems with one single-valued odd-symmetric nonlinearity and linear plant not having zeros in the transfer function, and named the dynamic HB. Based on the dynamic HB, first the equations for the amplitude, frequency, and amplitude decay of an oscillatory process in the Lure system are derived. It is then applied to analysis of rocking block decaying motions. An example is provided. I. INTRODUCTION Harmonic balance principle is a convenient tool for finding parameters of self-excited periodic motions. Due to this convenience, it is widely used in many areas of science and engineering. For a system with one nonlinearity and linear dynamics (Lure system), it can be illustrated by drawing the Nyquist plot of the linear dynamics and the plot of the negative reciprocal of the describing function (DF) [1] of the nonlinearity in the complex plane and finding the point of intersection of the two plots, which would correspond to the self-excited periodic motion in the system. Therefore, the harmonic balance principle treats the system as a loop connection of the linear dynamics and of the nonlinearity. It is also possible to reformulate the harmonic balance, so that the format of the system analyzed is not a loop connection but the denominator of the closed-loop system. This would imply a different interpretation of the harmonic balance, which would allow one to extend the harmonic balance principle to analysis of not only self-excited periodic motions but also other types of oscillatory motions. I. Boiko is with The Petroleum Institute, P.O. Box 2533, Abu Dhabi, U.A.E. (email: i.boiko@ieee.org ). Dynamic Harmonic Balance Principle and Analysis of Rocking Block Motions Igor M. Boiko