- #1
gaus12777
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Could you tell me the reason that if pole is close to the imaginary axis, (1) can be same as (2).
Why this approximation is correct?
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The discussion centers on the approximation validity when a pole is near the imaginary axis. It explains that the proximity of the roots to the imaginary axis indicates that the term 2ζpωp is small. This smallness allows for the simplification of equation (1) to equation (2) by ignoring that term. The reasoning hinges on the relationship between the real part of the quadratic equation and the behavior of the roots. Thus, the approximation holds true under these conditions.
Could you tell me the reason that if pole is close to the imaginary axis, (1) can be same as (2).
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The fact that the roots of (1) are close to the imaginary axis tells you (from the real part of the quadratic equation) that 2ζpωp is small. Ignoring that part of (1) gives (2).
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