The transient response of a misaligned rotor-coupling-bearing system passing through the critical speed has been analysed by using the finite element method (FEM) for flexural vibrations. The coupling has been modelled in two ways: a frictionless joint and a joint with stiffness and damping. From the vibration analysis, the subcritical speeds at one-half, one-third and one-fourth the critical speed have been found when the misaligned rotor-coupling-bearing system passes through its critical speed. The continuous wavelet transform (CWT) has been used as a tool to extract the silent features from the time response of the rotor system. A parametric study has been carried out to investigate the transient response of this rotor system for different angular accelerations in different types of misalignment.