A system is described by the transfer function H(s) = frac 10 s^2 + 2s + 10 . What is the natural frequency omega_n of this system?

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Electrical Engineering QUESTION #2145

Question 1

A system is described by the transfer function $H(s) = \frac{10}{s^2 + 2s + 10}$. What is the natural frequency $\omega_n$ of this system?

$10\text{ rad/s}$
$\sqrt{10}\text{ rad/s}$✔️
$2\text{ rad/s}$
$5\text{ rad/s}$

Correct Answer Explanation

Comparing with the standard form $\frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$, we see $\omega_n^2 = 10$, so $\omega_n = \sqrt{10}\text{ rad/s}$.

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