An electromechanical closed-loop control system has the

An electromechanical closed-loop control system has the following characteristic equation :
s³ + 6 Ks² + (K + 2) s + 8 = 0
where K is the forward gain of the system.
The condition for closed loop stability is

s³ + 6 Ks² + (K + 2)s + 8 = 0

For stablility,	(6K)(K + 2) - 8	= 0
	6

⇒ K > 0
∴ 3 K² + 6 K – 4 > 0

⇒ K =	-6 ± √36 + 48
	6

=	-6 ± √84	= 0.528 , -2.58
	6

Since K > 0, hence K = 0.528