Given T.F. H (s) = s + 2 / s2 + s + 4, under steady state

Given T.F. H (s) = s + 2 / s₂ + s + 4, under steady state condition, the sinusoidal input and output are respectively—
x (t) = cos 2t
y (t) = cos (2t + φ), then angle φ of will be

Given T.F.

H(s) =		Y (s)	=	s + 2	....(i)
		X (s)		s² + s + 4

x (t) = cos 2t
y (t) = cos (2t + φ)
from x (t) = cos 2t we concluded that ω = 2
on putting s = J ω = J 2. in equation (i) we get

H (2 J) =		2J + 2	=	2(1 + 1)
		–J² 2² + 2J + 4		– 4 + 2J + 4

=		2(1 + J)	= 2√2	∠ 45°
		2.J		∠ 90°

or	y (t)	= ∠ (45º– 90º) = ∠ – 45º
	y (t)