Analysis of combustion instability has traditionally been based on the assumption that linear coupling among acoustic modes is insignificant. While this is reasonable when one is interested in determining the unstable mode frequency and growth rate, in this paper we show that this assumption in a model-based active control design may lead to serious errors. To explain the origin of these errors, we employ both analysis and numerical examples to investigate the effect of linear coupling on the resonance and antiresonance properties of a benchtop premixed combustor in the presence of external excitation. The analysis is carried our using one-dimensional flow dynamics in the presence of an oscillating heat release source based on laminar premixed flame kinematics, and an external actuator in the form of a loudspeaker. We show that, for certain sensor-actuator configurations, a controller designed on the basis of a model where linear coupling is neglected may fail to suppress the thermoacoustic instability when coupling is present. In these cases, we find that the uncoupled model fails to predict the antiresonance damping in the system accurately and is therefore incapable of quantifying the system response to external excitation.