It is the ratio of maximum displacement of the forced vibration (x_{max}) to the deflection due to the static force F(x_{0}). 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/ω_{n} 
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 x_{0}) must be multiplied inorder to obtain the maximum amplitude of the forced vibration (i.e x_{max}) by harmonic force F Cos ωt.
x_{max }= x_{0 }X 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/C_{C }=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_{n }. Therefore magnification factor,