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  1. The system having the Bode magnitude plot shown in figure has the transfer function—


    1. 60 (s + 0·01)(s + 0·1)
      s2(s + 0·05)2

    2. 5(1 + 10s)
      s(1 + 20s)
    3. 8(s + 0·05)
      s(s + 0·1)(s + 1)
    4. 5(s + 0·1)
      s(s + 0·05)
Correct Option: D

From the given Bode-plot H(s) has a pole at ω = 0 and ω = 0·05
and zero at ω = 0·1.
Hence H(s) can be given as

H(s) =
K(s + 0·1)
s(s + 0·05)

By plot,
20 log10 |H(j0·01)| = 60
or
|H(j0·01)| = 103 = 1000.
or
2K(0·1 + j0·01)
∣ = 1000
j0·01(0·05 + j0·01)

or
K × 0·1
= 1000
0·01 × 0·05

or
K =
1000 × 0·01 × 0·05
= 5
0·1

Therefore,
H(s) =
5(s + 0·1)
s(s + 0·05)

Hence alternative (D) is the correct choice.



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