How can I approximate this transfer function?

AI Thread Summary
To approximate the transfer function, it is suggested that if a pole is close to the imaginary axis, it can be treated as having zero damping. This implies that the system behaves nearly purely oscillatory, allowing for the removal of the damping term (ζ) for simplification. The discussion raises questions about whether this approach is valid or if there are nuances that may be overlooked. The focus remains on understanding the implications of near-imaginary poles in system dynamics. Overall, the approximation method hinges on the assumption of minimal damping effects.
gaus12777
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I don`t know how can I approximate this transfer function
upload_2016-10-31_23-52-53.png

into this
upload_2016-10-31_23-53-35.png
In my book, pole is close to imaginary axis, so It can be approximated.
 

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Is that not just an assumption of having zero damping? If the pole is near the imaginary axis, the means the system would very nearly be purely oscillatory with no damping and you could just remove the ##\zeta## term to get an approximate answer. Unless I am missing something here...
 
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