Consider a single degree of freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle of the displacement with respect to the exciting force in degrees is
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Phase angle (\(\phi\)) transitions relative to frequency ratio (\(r = \frac{\omega}{\omega_n}\)):
- Low frequencies (\(r \ll 1\)): \(\phi \to 0^\circ\) (Response is in phase with force).
- At Resonance (\(r = 1\)): \(\phi = 90^\circ\) exactly, regardless of the value of damping ratio \(\zeta\) (provided \(\zeta > 0\)).
- High frequencies (\(r \gg 1\)): \(\phi \to 180^\circ\) (Response is out of phase).