Due to unbalance present in a rotating machinery, fluctuating stresses are generated leading to the formation of transverse cracks in rotors. The cracks propagate with the passage of time and increase the amplitude of vibration. High vibration amplitudes can give rise to rotor/stator rubs. During the rubbing phase, the crack propagation gets enhanced due to inter-connected nature of these faults. If left unattended, these faults can cause the premature failure of machine components. Hence, there is a need to develop fault detection mechanisms based on the vibration response so that these faults can be diagnosed during initial stages. The effect of gravity and the presence of cracks significantly changes vibration characteristics of the rotor, which is thoroughly investigated in this research for a two-degrees-of-freedom Jeffcott rotor. It has been observed that during rubbing, high harmonics are excited. These harmonics are integer multiple of the rotor spin frequency. Similar type of the response is also observed due to the presence of a transverse rotor crack. It is difficult to distinguish the type of faults based on the steady state dynamic response only. Instead of working only on a steady state vibration response, the transient vibration response during coasting up of the rotor is considered. During coasting up of the rotor, high harmonics are excited for both the crack as well as rotor/stator rubbing. The excitation of higher harmonics starts at much earlier in the spectrogram of the vertical response for the cracked rotor compared to that of rubbing. This fact is used in the development of a fault diagnosis technique based on Short Time Fourier Transform of the vibration response. The proposed technique can efficiently distinguish different types of faults even if multiple faults coexist.