In a linear mechanical system, all the vibration components will exist together, and none will interfere with any other. In the case of a non-linear system, the vibration components will interact and generate new components which are not in the forcing function. See also the section on linear systems in the Machine Monitoring chapter.

Vibration is the motion resulting from an oscillating force, and for a linear mechanical system, the vibration frequency will be the same as the forcing frequency. If there are several forcing frequencies occurring at the same time, then the resulting vibration will be a summation of the vibration at each frequency. Under these conditions the resulting waveform of the vibration will not be a sinusoid, and may be very complex.

Certain machines, especially very slow speed ones, produce vibration wave forms that are relatively easy to interpret directly. See also the section on Time Domain Analysis in the Machinery Monitoring chapter.

In the diagram, the high frequency and the low frequency vibration add together to make the complex waveform. In simple cases like this, it is relatively easy to find the frequencies and amplitudes of the two components by examination of the wave form, but most vibration signals are far more complex than this, and can be extremely difficult to interpret. In a typical rotating machine, it is often hard to get very much information about the inner workings of the machine by looking at the vibration wave form, although in certain cases wave form analysis is a powerful tool, as will be discussed in the chapter on machine vibration monitoring.