A computer implemented method of analysing tachometer and vibration response data from an apparatus having one or more rotary components, the method comprising the step of: providing vibration response data and corresponding tachometer data from the apparatus for a period over which a rotary component of the apparatus varies in rotational speed, the tachometer data being for that component; and repeatedly performing at intervals throughout the period the sub-steps of: determining a forcing frequency of the component from the tachometer data and a corresponding vibration response frequency of the apparatus from the vibration response data, comparing the forcing and vibration response frequencies to determine the relative phase difference between the frequencies, and determining the corresponding amplitude of the vibration response from the vibration response data; characterised in that the method comprises the further steps of: plotting the relative phase differences and vibration amplitudes on a polar diagram, whereby the plot trajectory is characteristic of the behaviour of the apparatus over the period; and comparing the plot trajectory with a reference trajectory for a period in which the apparatus experiences the same variation in rotational speed to account for phase shifts between the forcing frequency and the corresponding vibration response frequency. providing vibration response data and corresponding tachometer data from the apparatus for a period over which a rotary component of the apparatus varies in rotational speed, the tachometer data being for that component; and repeatedly performing at intervals throughout the period the sub-steps of: determining a forcing frequency of the component from the tachometer data and a corresponding vibration response frequency of the apparatus from the vibration response data, comparing the forcing and vibration response frequencies to determine the relative phase difference between the frequencies, and determining the corresponding amplitude of the vibration response from the vibration response data; determining a forcing frequency of the component from the tachometer data and a corresponding vibration response frequency of the apparatus from the vibration response data, comparing the forcing and vibration response frequencies to determine the relative phase difference between the frequencies, and determining the corresponding amplitude of the vibration response from the vibration response data; characterised in that the method comprises the further steps of: plotting the relative phase differences and vibration amplitudes on a polar diagram, whereby the plot trajectory is characteristic of the behaviour of the apparatus over the period; and comparing the plot trajectory with a reference trajectory for a period in which the apparatus experiences the same variation in rotational speed to account for phase shifts between the forcing frequency and the corresponding vibration response frequency. plotting the relative phase differences and vibration amplitudes on a polar diagram, whereby the plot trajectory is characteristic of the behaviour of the apparatus over the period; and comparing the plot trajectory with a reference trajectory for a period in which the apparatus experiences the same variation in rotational speed to account for phase shifts between the forcing frequency and the corresponding vibration response frequency.