The aim of the present work is to study possible responses of a system with combustion to different disturbances under the conditions when the initial regime is characterized by damped oscillations. Mathematically the problem is formulated by a system of ordinary differential heat and mass balance equations. Damped oscillations, appearing in a model on instantaneous perturbation, are characterized by the natural frequency of the system, while the ability to remember perturbations as oscillations is represented by the quality factor. Linear analysis allows one to relate the parameters of a chemically reacting system. Resonance properties of the system with combustion are studied, the resonance phenomena are established at frequency multiples and subharmonics, the beating and parametric excitation of oscillations are found, and the system sensitivity to the shape of the perturbative signal and different perturbative parameters is studied. The results obtained can be used for controlling combustion intensity in a continuously stirred tank reactor.