1 a F(s)
.
=
.
6
G(s)
.
si 2(F) et
20
0 i5
=
,
=, 2"(G) ecost 05
2" (FG) 9.elt 2)code D
-
=
ecodz
=
.
F(S)
=
[ e(sinz 2cs2)]
+
.
+
,
-
.
2
Fe(sint 2 cost) jet D
=
.
e
it ! e* (sint 2 cost) etf
=
b
+
=
-
+
si 2" (F) etas
:
,
= 2 2"(G)
G(s)
=
sint
a.5
,
2"(76) %est-?sinzdz
=
=
ete2Sindi &
Fetesicos 3 2(y) Y 21y') SY
=
=
,
2(r)
D
"
e-4s) est retsdt
=, _ Exs[ edt =, Ex-sessi
=, _
.
-
-
=> SY + 9Y=
y
=
ez
e
4)
-
e
et
-
-
e
4
1- e-43 S (S + 9)
.
=
.
2)(sis+) ).d
=
,
0 .5
=
=
(e)(l+ e ) 3 1s +9)
+
·
.
1- e+ +
....
0
15
(e)
e*
=
2"(5)
e
=
2"(5) 1
Hers
4
(1-e S)( -3)
-
:
(e e * e * ess,
-
S(S+ 9)
0 .5
then use 2nd
shifting
2" (e
Sista)
2)
05
e-9(t
(
u(t
q(1
2)
-
=
.
-
.
-
sita) = (1-e9(t-4)) u(t-4)0
2" (e *
.
5
.
:
-
+
y(t) 2 (y)
&(1 e
=
=
9(t
2)) u(t 2) -(1 e9ht 4)) u(t 4)
-
-
-
-
.
-
-
-
.
of
on
↑(1 e-9(t b) u(t 6) 5)) e9(t 8)) u(t 8)
-
+
-
-
.
-
-
-
...
f
sketch
Yx
-
. ty" + y +
3
5
-
''s
I
2
in't
o
ty 0 = Soln Jolt)
:
=
2 Ity) -Y D
21y') SY-b
=
=
2(y") 52Y S
=
-
2(ty") -d(5y-S)
=
=
2SY
-
F-
-
= -
5-Y+ 1 + SY 1 Y 0
-
-
S
Y(5)
i 24
=
=
14 fls+
32 [IJolt) D
:
,
y10) 1 Y 10)
=
,
ISY-S+
.
D
=
0
,
i:
y It) must
be Jolt)
.
-
14T
I
rank (A) 3 ,
nullity (A)
D
=
3 3
-
65xz 195
= X=3
742
477X22
-
-
=
=
-
11 3
=
.
x, + 2 2 + 3 3
.
an
.
=
14
= x1 =
unique soln for
,
=
0
D
(
D