## Step response of a second-order system with respect to the damping ratio ζ (the poles are shown as X).

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(a) Overdamped oscillation. The damping ratio is greater than 1 and the poles are both negative real numbers. The system reaches its steady state without oscillation. As the damping ratio increases, it reaches the steady state slower. (b) Undamped oscillation. Note that all the poles are on the imaginary axis. The damping ratio is zero and there is an oscillation without damping. (c) Underdamped oscillation. The damping ratio is between 0 and 1, and the poles are complex numbers with the negative real part. The oscillation gradually decreases to zero as the system reaches its steady state. (d) Critically damped oscillation. The steady state is reached in the fastest way without oscillation. The two poles have the same negative value [42].