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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 transfer function G(s) has a gain that decreases with frequency, which is characteristic of a second-order system, indicated by the s² term in the denominator. The negative phase across all frequencies further supports that G(s) is a type of low-pass filter, consistent with the behavior of a second-order system.

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