A certain fourth$-$order model has the roots

$s=-2+-4j,-10+-7j$

Identify the dominant roots and use them to estimate the system's time constant, damping ratio, and oscillation frequency.

$\frac{5\mathrm{.}77}{7\mathrm{.}69}$

points awarded

a$.s=-2+-4j$

Scored

b$.s=-10+-7j$

The dominant root is

The system's time constant $(T)$ is

and oscillation frequency $({}_d)$ is

$($x$)$ rad$/$s$.$