Module 9 : Forced Vibration with Harmonic Excitation; Undamped Systems and resonance; Viscously Damped                    Systems; Frequency Response Characteristics and Phase Lag; Systems with Base Excitation;                    Transmissibility and Vibration Isolation; Whirling of Shafts and Critical Speed.
Lecture 1 : Harmonic vibration of single DOF system
Now we introduce the notation
   undamped natural frequency

frequency ratio

critical damping

damping factor

  we can rewrite equations 9.1.9 and 9.1.10 as
 
(9.1.11)
 
and
(9.1.12)
 

If we consider that the force of magnitude F0 were applied statically, the response would then be

 
 
(9.1.13)
 

Thus re-writing eq (9.1.11), we get,

 
 
(9.1.14)
 


Fig 9.1.4 Variation of dynamic magnification factor with frequency ratio

  Since the R.H.S. indicates by how much the dynamic response is more than the static response, it is usually termed the Magnification Factor. If we now plot the variation of the magnification factor with frequency of excitation, we get a curve as shown in Fig. 9.1.4. There are primarily three regions of interest in such a graph.
   
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