Question:
The transfer function of a system is given by:
\[
\frac{Y(s)}{X(s)} = \frac{10}{s^2 + 3s + 10}
\]
What is the damping ratio of the system?
The transfer function of a system is given by:
\[
\frac{Y(s)}{X(s)} = \frac{10}{s^2 + 3s + 10}
\]
What is the damping ratio of the system?
Show Hint
For a second-order system, the damping ratio $\zeta$ can be calculated from the coefficient of $s$ and $\omega_n$ (natural frequency).
Updated On: Jun 17, 2025
- 0.5
- 0.3
- 0.2
- 0.7
Show Solution
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The Correct Option is A
Solution and Explanation
The transfer function is in the form: \[ \frac{10}{s^2 + 2\zeta \omega_n s + \omega_n^2} \] Comparing coefficients, $\omega_n^2 = 10$ and $2\zeta \omega_n = 3$.
Thus, $\omega_n = \sqrt{10}$ and $\zeta = \frac{3}{2\sqrt{10}} \approx 0.5$.
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