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Electrical Engineering QUESTION #2158
Question 1
The transfer function of a second-order system is $H(s) = \frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$. For $\zeta = 0.5$ and $\omega_n = 10\,\text{rad/s}$, the percent peak overshoot in a unit step response is:
  • $16.3\%$✔️
  • $4.3\%$
  • $25.4\%$
  • $9.5\%$
Correct Answer Explanation
$\%PO = e^{-\pi\zeta/\sqrt{1-\zeta^2}} \times 100 = e^{-\pi(0.5)/\sqrt{0.75}} \times 100 = e^{-1.814} \times 100 \approx 16.3\%$.