The Bode plot of a first-order system indicates that the corner frequency is (2.25 mathrm{rad} / mathrm{sec})

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The Bode plot of a first-order system indicates that the corner frequency is \(2.25 \mathrm{rad} / \mathrm{sec}\) and the approximate low-frequency logarithmic magnitude is \(-23.10 \mathrm{~dB}\).

a. Find the transfer function.

b. Using the results of (a), find the approximate value of the logarithmic gain at \(\omega=100 \mathrm{rad} / \mathrm{sec}\).

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