A system is described by the following transfer function:

$G(s)=\frac{{}_n^2}{s^2+2{}_{n}s+{}_n^2}$

a$)$ Determine the region of poles in the complex plane if:

i$)$ Percent overshoot is to be less than $4\mathrm{.}32\%,$

ii$)$ Settling time based on $2\%$ criterion is to be less than $2$ seconds.

b$)$ Now, in addition to the above requirements, the following conditions are also required:

i$){}_n=4ra\frac{d}{s}$

ii$)t_p=3\mathrm{.}14s$

Is it possible to satisfy all four conditions together? If it is possible, where would the poles be located in the complex plane.