Question
A viscously damped single-degree-of-freedom system with positive damping is driven by a harmonic force at its undamped natural frequency, ω = ωn = √(k/m). In steady state, the phase lag of displacement relative to the applied force is
The correct answer is
90°
For positive viscous damping, the dynamic stiffness is \(k-m\omega^2+i c\omega\). At ω = ωn = √(k/m), its real part vanishes, so displacement lags the harmonic force by 90°.
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