Of the following transfer functions of second order linear time-invariant systems, the underdamped system is represented by
- A. $H(S)=\frac{1}{S²+4S+4}$
- B. $H(S)=\frac{1}{S²+5S+4}$
- C. $H(S)=\frac{1}{S²+4.5S+4}$
- D. $H(S)=\frac{1}{S²+3S+4}$
Answer: D. $H(S)=\frac{1}{S²+3S+4}$
Explanation: Comparing $H(s)=\frac{1}{s²+3s+4}$ with standard form $H(s)=\frac{\omega_n^2}{s²+2\xi\omega_ns+\omega_n^2}$, we get $2\xi\omega_n=3$ and $\omega_n=2$. Thus, $\xi=\frac{3}{4}=0.75$. Since $\xi<1$, the system is underdamped.