prueba de edo
DESCRIPTION
hukkjkTRANSCRIPT
-
1.-Dada la siguiente funcin:
() = {
2 0 < 22 + 8 2 < 4
+ 2 4 < 63 + 15 6 < 7
a) Dibujar f(t), fI (t) y fII(t)
b) Calcular: {()}, {()}, {()}
a) ()
c)()
c)()
-
() = 2() 4( 2)( 2) + 3( 2)( 4) (4 13)( 6) (3 15)( 7)
() = 2() 4( 2)( 2) + 3( 4 + 2)( 4) (4 13)( 6) (3 15)( 7)
{f(t)} =2
2
42
2+
34
2
64
6{4( + 6) 13} 7{3( + 6) 15}
{f(t)} =2
2
42
2+
34
2
64
6 (
4
2
11
) 7 (
3
2
3
)
() = 2() 4( 2) + 3( 4) 4( 6) 3( 7)
{(t)} =2
42
+
34
46
37
() = 2() 4( 2) + 3( 4) 4( 6) 3( 7)
{(t)} = 2 42 + 34 46 37
2. Resolver el siguiente sistema de ecuaciones diferenciales:
a) Utilizando la Transformada de Laplace.
b) Por reduccin a una ecuacin de segundo orden.
{() = () () + ; () =
() = () + () + ; () =
() = () () +
() = () () +
() () + = () + (() () + ) +
() () () = ( + )
( + )() = ( + )
() = { () + ()}
-
() =
+ |
=
+ |
=
() =
() = { () + ()}
() = {1( sin() 2 cos()) + 2(cos() 2 sin())} +
1
10
() = { () + ()}
(1( sin() 2 cos()) + 2(cos() 2 sin())) +
1
10 +
() = {1 cos() + 2 sin() + 1 sin() + 21 cos() 2 cos() 22 sin()} +
1
5
() = {1(3 cos() + sin()) 2(3 sin() cos())} +
1
5
1 = 1 1 1
10 1 =
21
10
0 = 31 2 + 1 1
5 1 =
71
10
() = {
() +
()}
() = {21
10(3 cos() + sin())
71
10(3 sin() cos())} +
1
5