Why Does the Bode Plot of a Type 1 System Show a Damped Slope Initially?

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SUMMARY

The discussion focuses on the Bode plot characteristics of a Type 1 system represented by the transfer function G(s) = 100 / (s(s+5)). It establishes that the initial magnitude in dB can be calculated using the formula 20log(numerator/denominator) at s = 0. The forum participants clarify that while a Type 0 system exhibits a consistent decrease of 20 dB per decade, a Type 1 system's slope decreases by 40 dB per decade after an initial damped slope. The initial amplitude is derived from the expression 100 / √(25ω² + ω⁴), indicating a damped response at low frequencies.

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For a transfer function of G(s) = 100 / (s(s+5)), I'm having trouble finding the initial magnitude in dB. It's a type 1 system. If it was a type 0 system with only (s+5) in the denominator, the initial magnitude would be 20log(nominator/denominator) where s is an element of 0, and would decrease by 20 dB per decade. For the system 1, the magnitude should decrease by 40 dB each decade. However, most transfer functions which I've bode plotted in wolfram alpha, appear to have a slightly damped slope until it reaches 0 db, before decreasing at a steady rate of 40dB.

Care to explain how I find the initial magnitude?

[This is NOT homework, but research of (art of) bode plotting transfer functions with denominator of higher order]
 
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G(s) = 100/(s² + 5s)
Let s ← jѠ

G(s) = 100/(-Ѡ² + j5Ѡ)

amplitude = 100/ √(25Ѡ² + Ѡ⁴)
      = 100/(5Ѡ √(1 + Ѡ²/25)) 

At low frequencies where Ѡ « 5, amplitude ≈ [PLAIN]https://www.physicsforums.com/images/icons/icon5.gif [PLAIN]https://www.physicsforums.com/images/icons/icon5.gif

How many dB/decade will the slope of this be in the region Ѡ « 5?
 
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