16 views

0 votes

Two linear time-invariant systems with transfer functions

$$G_{1}(s) = \frac{10}{s^{2}+s+1} \; \text{and} \; G_{2}(s) = \frac{10}{s^{2}+s\sqrt{10}+10}$$

have unit step responses $y_{1}(t)$ and $y_{2}(t),$ respectively. Which of the following statements is/are true?

- $y_{1}(t)$ and $y_{2}(t)$ have the same percentage peak overshoot.
- $y_{1}(t)$ and $y_{2}(t)$ have the same steady-state value.
- $y_{1}(t)$ and $y_{2}(t)$ have the same damped frequency of oscillation.
- $y_{1}(t)$ and $y_{2}(t)$ have the same $2\%$ settling time.