The unit-step response of a dynamic system is shown in Figure 10.13. The maximum value of the response is 1.1 and its steady-state value is 0.95 . The response reaches \(10 \%\) and \(90 \%\) of its steady-state value at 0.048 and \(0.21 \mathrm{~s}\), respectively. Find the transfer function of the system if it can be approximated as \(a /\left(s^{2}+2 \zeta \omega_{n} s+\omega_{n}^{2}\right)\).

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FIGURE 10.13 Problem 8. Amplitude 1.2 1.1 0.8 0.6 0.4 0.2 0 0 1 0.95 0.048 0.21 0.2 L 0.4 0.6 Time (s) 0.8 1 1.2