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
Free Vibration of Two d.o.f. Systems
 

In the previous modules we discussed the free and forced vibration behavior of single d.o.f. systems. In this lecture, we will extend the discussion to two d.o.f systems. We will begin with free vibrations. We will be interested in determining how the system vibrates given some initial disturbance and left free to vibrate on its own. We will thus determine the natural frequencies of vibration etc. We had observed earlier that damping has marginal effect on natural frequency of single d.o.f system but primarily controls the resonance amplitudes. Thus we will consider undamped two d.o.f. system for our discussion.

 


Fig 10.1.1 A two d.o.f. spring mass sysytem

 

Consider a two d.o.f. spring-mass system as shown in Fig. 10.1.1 with two masses and three springs. To specify the configuration of the system, we need to specify the position of both the masses and hence we refer to this as a two d.o.f system.

   
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