“Introduction:

Every machine or structure has a Natural Frequency, a physical property of mass, stiffness, and damping. Every machine or structure is not necessarily in “resonance”. Webster did good:

Resonance can be good or bad. For machines or structures it is generally bad. The stimulus can be very small- “self excited” in some “instability” cases.

A vector diagram can be used to represent forced vibration with viscous damping. Three (3) diagrams will be shown later representing the condition of a frequency well below resonant frequency, at resonance, and a frequency well above resonance. These diagrams will attempt to correlate the Amplification Factor and phase changes as they relate to a Bode’ diagram or a balancing chart using Bode’ and Polar Data.

There are certain factors to understand about the Force Vector as it explains many things about vibration (acceleration, velocity, & displacement) and a rotor’s response during acceleration or de¬celeration . 

The Vector Diagram above represents a rotor operating below its 1st resonance (critical)(natural frequency).

"Amplification (Magnification) Factor Vs. Frequency Vs Phase:

Below is a forced response plot of a damped system, it represents the response X/Xo plotted against the frequency ratio, ω/ωn, [@ 1.0 = resonance]. Further, the phase change is shown for different percentages of damping ,C, respective to critical damping, Cc.”