# Why this approximation is correct?

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1. Dec 4, 2016

### gaus12777

Could you tell me the reason that if pole is close to the imaginary axis, (1) can be same as (2).

2. Dec 5, 2016

### FactChecker

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).