An analytical frame work is developed to understand and predict the thermoacoustic instability in solid rocket motors, taking into account the non-orthogonality of the eigenmodes of the unsteady coupled system that comprises of the acoustic field and the propellant burn rate dynamics. In general, thermoacoustic systems are non-normal leading to non-orthogonality of the eigenmodes. For such systems, classical linear stability predicted from the eigenvalue analysis is valid only in the asymptotic (large time) limit. However, the short term dynamics can be completely different and a generalized stability theory is needed to predict the linear stability for all times. Non-normal systems show initial transient growth for suitable initial perturbations even when the system is stable according to classical linear stability theory. The terms contributing to the non-normality in the acoustic field and unsteady burn rate equations are identified. These terms, which were neglected in the earlier analyses, are incorporated in the present analysis. Furthermore, the short term dynamics is analysed using a system of differential equations that couples the acoustic field and the burn rate, rather than using ad hoc response functions which were used in earlier analyses. In the present case, an SRM with homogeneous propellant grain is analysed. Nonlinearities in the system are incorporated by including second order acoustics and a physics based nonlinear unsteady burn rate model. Nonlinear instabilities are analysed with special attention given to 'pulsed instability'. Pulsed instability is shown to occur with pressure coupling for burn rate response. Transient growth is shown to play an important role in pulsed instability.