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
  

Fig 10.1.2 Free body diagrams for a two d.o.f. system
 

The free body diagrams are shown in Fig. 10.1.2. Using Newton 's second Law, we write the equations of motion of each mass as follows:

 

10.1.1
 

Using matrix notation, we can re-write as follows:

 
10.1.2
 

Thus we have two coupled, second order ordinary differential equations of motion with constant coefficients.

   
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