Module 10 : Vibration of Two and Multidegree of freedom systems; Concept of Normal Mode;
                      Free Vibration Problems and Determination of Ntural Frequencies;
                      Forced Vibration Analysis; Vibration Absorbers; Approximate Methods -
                      Dunkerley's Method and Holzer Method
Lecture 1 : Free Vibration of Two d.o.f. systems
Physical Meaning of Normal Modes
  We can attribute the following physical meaning to the mathematical solution obtained above – if we give initial conditions such that the two amplitudes are in the ratio given above (either eq. (10.1.13 ) or (10.1.15 )) and leave the system free to vibrate on its own, it will continue to vibrate forever maintaining this ratio of amplitudes all the time. This free vibratory motion will be at the frequency or respectively. These are known as the natural modes of the system – two for a two d.o.f system and in general “n” for an “n” d.o.f. system. For the present case, these are depicted in Fig. 10.1.3
 



Fig 10.1.3 Depiction of Mode Shapes (Normal modes)

 

It must be appreciated that these are only ratios of amplitudes of the two masses and not absolute magnitudes of vibratory displacement. Thus they indicate a certain shape of vibrating system rather than any particular amplitudes and hence they are also known as Mode Shapes.

   
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