Obtain the transfer function for the response curve shown

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Obtain the transfer function for the response curve shown below—

1. 40
  s(1 + 0·1s)
2. 4
  s(1 + 0·1s)
3. 4
  s(1 + 0·01s)
4. 20
  s(1 + 0·1s)

Correct Option: C

From figure
20 log₁₀ K = 12
K = 10^12/20
or K = 3·98 ≈ 4
one pole atω = 100
i.e., (1 + sT),
where
T₀ = 1/ω = 1/100
(1 + 0·01s)
Hence transfer function, G(s) H(s) = 4/1 + 0·01s
Hence alternative (C) is the correct choice.