$(1)$ If $\frac{Y(s)}{x(s)}=\frac{4(s+1)}{(s+3)(s+4)}$ receives and input $x(t)=2sin(3t),$ the output $y(t)$ at steady state will be : $y(t)=q,$

$(2)$ In a unit feedback system, if the open loop transfer functions is given by $HG(s)=\frac{K}{s^2(s+2)},$ if the Nyquist path and plot are shown, check the stability of this system

$(3)$ Consider the closed$-$loop system shown. G$($s$)$ has no poles in the right$-$half s plane.

$(4)$

$($i$)$ If the Nyquist plot of G$($s$)$ is as shown in Fig. $5-$a is this system stable?

$($ii$)$ If the Nyquist plot is as shown in

Fig. $5-$b$,$ is this system stable?