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
For a non-trivial solution, we can write,
 
10.1.6
 

Therefore we have the frequency equation / Characteristic equation:

 
10.1.7
 
10.1.8
  The “natural frequencies” of the system are obtained as the solutions of the characteristic frequency equation as follows:
 
10.1.9
 
10.1.10
  when    
  we get