Every moving system has some amount of vibration. This is a natural result of unbalanced components,rubbing, reversals, etc.
Some vibrations are very predictable, and can be estimated mathematically, and their effects compensated for.
Mathematically a vibration is a displacement/force/velocity/acceleration of small amplitude that will ‘shake’ and object.
The most significant vibration in engineered systems is periodic. In these systems there is often an approximate spring-mass-damper system that gives us a second order response to disturbances.
In vibration modeling we typically assume that all components are linear. In a linear system the forcing (input) frequencies are directly related to response (output) frequencies.
In non-linear vibration systems we end up with the frequency of the forcing function being transformed to other frequencies. This tends to make the vibrations seem less clear, and appear more chaotic.
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