Tuesday, 11 October 2016

Magnification Factor (or) Dynamic Magnifier

It is the ratio of maximum displacement of the forced vibration  (xmax) to the deflection due to the static force F(x0). We have proved in the previous article that the maximum displacement or the amplitude of forced vibration. Relation between magnification factor and phase angle for different values of ω/ωn
Magnification factor or dynamic magnifier,

The magnification factor or dynamic magnifier gives the factor by which the static deflection produced by a force F (i.e x0) must be multiplied in-order to obtain the maximum amplitude of the forced vibration (i.e xmax) by harmonic force F Cos ωt
xmax xX D
Above Fig shows the relation between the magnification factor (D) and phase angle Φ for different value of and for  values of damping factor  C/CC =0.1, 0.2, and 0.5.

Note: 1. If there is no damping (i.e if the vibration is undamped), then c=0. In that case, magnification factor,
2. At resonance, ω/ω. Therefore magnification factor,