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?

• A. 0.5
• B. 0.3
• C. 0.2
• D. 0.7

Hint:

For a second-order system, the damping ratio $\zeta$ can be calculated from the coefficient of $s$ and $\omega_n$ (natural frequency).

Answer 1

The Correct Option is A

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 $\zeta = \frac{3}{2\sqrt{10}} \approx 0.5$.