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 $p^\ast$ 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: $\omega_n = 3$ rad/sec and $\theta = 60^{\circ}$

System 2: $\omega_n = 1$ rad/sec and $\theta = 70^{\circ}$

Which one of the following statements is correct?

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first-order pole-only approximation such that the steady-state values of the unit step responses of the original and the approximated systems are same?

The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as $$\xi$$ and $$\omega$$_{n} are