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taofeng,
Qualitative Explanation:
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An underdamped system yields an exponentially decreasing sinusoidal output in response to a step input
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A critically damped system the minimum amount of damping that will yield a non-oscillatory output in responce to a step input.
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An overdamped system also yields a non-oscillatory utput in response to a step input, but has more damping than necessary to achieve the non-oscillatory output.
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For a second order linear system, the transfer function can be written in the form
1/[s^2 + 2Z(w0)s + (w0)^2]
Where
. w0 is the undamped natural frequency
. Z (Zeta) is the damping factor
A critically damped system is represented by a damping factor of 0.707.
please see the pictures of this link and you will learn what is the meaning of damping response . It is a behaviour of respone of system to step function
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