Free Vibration of MDOF Systems
Why free vibration takes place at MDOF system?
Expert
Free Vibration of MDOF Systems:Free vibration take place at natural frequencies of the system and, in general, the motion will consist of several simultaneous oscillations at the various natural frequencies of the system.
However, under certain specific conditions, all the coordinates will undergoes harmonic motion corresponding to one of the normal frequencies of the system.
When such motion take place, the motion is called the principal mode of vibration, or the normal mode of vibration.
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(a) The response for an undamped single degree of freedom system under free vibration is given as where ωn is the natural frequency and A and B are unknown that can be determined from the initial conditions. The response 
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