Consider the standard second-order system of the form $\frac{\omega_{n}^{2}}{s^{2}+2 \zeta \omega_{n} s+\omega_{n}^{2}}$ with the poles $p$ and $p^{*}$ having negative real parts. The pole locations are also shown in the figure. Now consider two such second-order systems as defined below:
System $1$: $\omega_{n}=3 \mathrm{rad} / \mathrm{sec}$ and $\theta=60^{\circ}$
System $2$: $\omega_{n}=1 \mathrm{rad} / \mathrm{sec}$ and $\theta=70^{\circ}$
Which one of the following statements is correct?
- The settling time of System $1$ is more than that of System $2$.
- Settling time of System $2$ is more than that of System $1$.
- Settling times of both the systems are the same.
- Settling time cannot be computed from the given information.