A SYSTEM WAS A CHARACTERISTIC EQUATION:

$D(s)=s^3+k{s}^2+(1+k)s+6=0$

WHERE $K$ IS A CONSTANT.

DETERMINE THE RANGE OF $K$ FOR A STABLE SYSTEM

$2.$ A SYSTEM IS REPRESENTED BY THE BLOCK DIAGRAM SHOWN BELOW:

DETERMINE THE RANGE OF $K$ FOR A STABLE SYSTEM

$3.($a$)$ A SYSTEM HAS THE SECOND$-$ORDER CHARACTERISTIC Equation:

$s^2+as+b=0$

WHERE a AND $b$ ARE CONSTANT PARAMETERS DETERMINE THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE SYSTEM TO BE STABLE. SHOW YOUR PROOF IN DETAIL.

$(8)$ BASED ON YOUR RESULT IN $($a$)$ ABOVE, IS IT POSSIBLE TO DETERMINE THE STABILITY OF A SECOND$-$ORDER SYSTEM SUST BY INSPECTING THE COEFFICIENTS OC

THE CHARACTERISTIC EQUATION?