The Phasor Analysis Method For Harmonically Forced Linear Systems

One of the most common tasks in vibration analysis is the determination of the steady-state response of a system to harmonic forcing. This is also true in AC electrical circuit analysis. The most common case encountered in vibration engineering is that of the forced underdamped system. In this case, the transient portion of the response vanishes exponentially as e−ζωt, where ζ is the so-called dimensionless damping constant, and for the underdamped case, 0 < ζ < 1. The prototypical mass-spring-damper system is shown in Figure 1, where in the harmonically forced case, we shall assume that F (t) = F0 sinωt, where ω is the forcing frequency in radians second .