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The Bode plot of a transfer function G(s) is shown in the figure below. The gain (20 log |G(s)|) is 32 dB and -8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ω. Then G(s) is

1. 39.8 / s
2. 39.8 / s²
3. 32 / s
4. 32 / s²

Correct answer: 39.8 / s²

Solution

The correct option is right because the transfer function G(s) = 39.8 / s² indicates a second-order system with a gain that decreases with frequency, which aligns with the given Bode plot characteristics of a gain of 32 dB at low frequencies and -8 dB at higher frequencies, along with a consistently negative phase.

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