+ x, and represent the harmonic excitation as the real part

The above complex expression for the harmonic amplitude can be expressed as a magnitude and phase lag:

These expressions for the whirl magnitude and phase angle could also be developed by assuming a steady-state harmonic response W = Aeifl' in the Z direction and substituting into Eq. (5). The vector sum of the V and W displacements over time is thus a circular whirling motion in the direction of rotation.