A discussion of vibration theory usually begins with the analysis of a simple mass, spring and damper system. This is because once you analyze the vibration process for this system you can then apply the results to the most complicated vibrating structure. It will be shown later how complex structures vibrate in a superposition of a unique set of different deformation patterns (called mode shapes). Each mode shape has its own resonance frequency and responds to vibratory forces in a manner described by the same differential equations as are used to describe single mass, spring and damper vibration response.

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