2-1
试建立图所示电路的动态微分方?
+
C
?
-
-
u
i
u
o
R
1
R
2
i
1
i
i
2
+
C
?
-
-
u
i
u
o
R
1
R
2
i
1
i
i
2
L
u
1
解:
u
1
=u
i
-u
o
i
2
=C
du
1
dt
i
1
=i-i
2
u
o
i=
R
2
u
1
i
1
=
R
1
=
u
i
-u
o
R
1
dt
d
(
u
i
-u
o
)
=C
(a)
u
C
d
(
u
i
-u
o
)
dt
u
o
-
R
2
=
i
-u
o
R
1
i=i
1
+i
2
i
2
=C
du
1
dt
u
o
i
1
=
R
2
u
1
-u
o
=
L
R
2
du
o
dt
R
1
i=
(
u
i
-u
1
)
(b)
解:
)
-
R
2
(u
i
-u
o
)=R
1
u
0
-CR
1
R
2
(
du
i
dt
dt
du
o
CR
1
R
2
du
o
dt
du
i
dt
+R
1
u
o
+R
2
u
0
=CR
1
R
2
+R
2
u
i
u
=
R
1
i
-u
1
u
o
+C
R
2
du
1
dt
u
1
=u
o
+
L
R
2
du
o
dt
u
du
o
dt
R
1
R
2
L
du
o
dt
+
CL
R
2
d
2
u
o
dt
2
=
-
-
i
R
1
u
o
R
1
u
o
R
2
+C
)u
o
R
1
R
2
L
du
o
dt
)
CL
R
2
d
2
u
o
dt
2
=
+
+(
u
i
R
1
1
R
1
1
R
2
+(C+
2-2
求下列函数的拉氏变换?/p>
(1) f(t)=sin4t+cos4t
L
[
sin
ω
t
]
=
ω
ω
2
+s
2
=
s+4
s
2
+16
L
[
sin4t+cos4t
]
=
4
s
2
+16
s
s
2
+16
+
s
ω
2
+s
2
L
[
cos
ω
t
]
=
解: