Discussion
For overdamped systems, the damping ratio is always ______.
Answer: D
The damping ratio \(\zeta\) of a second order system decides the nature of the response. For \(\zeta = 0\) the response is undamped, for \(0 < \zeta < 1\) it is underdamped (oscillatory with decaying amplitude), for \(\zeta = 1\) it is critically damped, and for \(\zeta > 1\) the system is overdamped.
In the overdamped case the characteristic roots are real and unequal, and the response creeps to its final value without overshoot. So the damping ratio of an overdamped system is greater than unity, option D.
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