Prediction of limit cycle of combustion instability could be achieved by the examination of the nonlinear flame response to the acoustic oscillations within the combustor. This study uses the flame describing function framework to examine the effects of the forcing frequency and the fundamental frequency of the duct on the magnitude of the dominant acoustic modes of the combustion chamber. Results showed a phenorminal influence of the forcing frequencies on the magnitude of the dominant acoustic modes of the combustor with respect to its fundamental frequency, which are in agreement with recent studies. Results of this kind provide a promising novel approach to alienating instability boundaries in a combustion system.