Transformada de laplace

1. Transformada de Laplace (ejemplos I) Página: 1 de 2
1 Calcular las transformadas de Laplace
2 Calcular la transformada inversa de Laplace
14/10/16
b.− f (t )=[2 t+4]u(t)+3δ (t )a.− f (t)=[5]u(t)
c.− f (t )=[3t
2
−5t +6]u(t ) d.− f (t)=[3t
3
+6e
−5t
]u(t )
e.− f (t)=[6 t
4
e
3t
+5t
2
e
−2t
]u(t) f.− f (t)=(t
2
+5t−3)e
−5t
u(t )
g.− f (t )=[3 sin(5t)+5 cos(5t )]u(t)
j.− f (t )=e
−3t
sin(4t )u(t )
k.− f (t )=e
−3t
[sin(4t )−3cos(3t)]u(t ) l.− f (t)=[(t−5)
2
+2(t−5)]u(t)
a.− F (s)=
1
s
3
b.− F(s)=
1
s
2
+
48
s
5
c.− F (s)=
(s+3)
2
s
3
d.− F (s)=
2
s
2
−
5
s
+
7
s−2
e.− F (s)=
5
4s+6
f. −F(s)=
10
s
2
+49
g.− F(s)=
12s
s
2
+16
h.− F(s)=
3s+6
s
2
+9
m.− f (t)=u(t −1)
o.− f (t)=[t−4]u(t−2)
j.− F(s)=
5
s
2
+6s+13
i.− F (s)=
5
(s+2)
3
p.− f (t)=e
−2(t−5 )
u(t−5)
n.− f (t )=(t −3)u(t −3)
i.− f (t)=[3+4e
−t
−5 e
4t
]u(t)
h.− f (t )=(1+e
−2t
)
2
u(t)
k.− F(s)=
e
−2s
s
3
m.− F(s)=
2s−1
s(s+1)
2
l.− F (s)=
2 s+3
s(s+1)
n.− F(s)=
s−5
(s+1)(s
2
+2)
o.− F (s)=
2s+3
s (s
2
+2s+26)
p.− F (s)=
s
2
+4
(s+1)(s+2)(s
2
+4s+20)
q.− f (t)=6 [2−3 cos(2t)]u(t ) r.− f (t)=e−5t
cos(2t)u(t)
s.− f (t )=3cos (5t+π /3)u(t) t.− f (t )=
t
3
e
4t
u(t )

2. Transformada de Laplace (ejemplos I) Página: 2 de 2
3 Hallar la transformada de Laplace de la función f(t) definida por:
4 Resolver las ecuaciones diferenciales siguientes:
a)
b)
c)
d)
e)
f)
g)
14/10/16
a)
para
para
para
c)
para
para
para
para
¨y+2 ˙y +2 y=0 y(0)=5 ; ˙y (0)=−2
˙y+y=1 y(0)=0
2 ˙y +3 y=5 y(0)=2
˙y+2y=t y(0)=−1
¨y+3 ˙y +6 y=5⋅sin(10t) y(0)=2 ; ˙y (0)=25
¨y+4 ˙y +4 y=t
3
e
2t
˙y(0)=0 ; y (0)=0
˙y(t )+6 y (t )+9∫
0
t
y (τ )dτ =2 y(0)=0 ;∫
0-
0
+
y (t )d t=0
f (t )=5 0<t<3
f (t )=0 t≥3
f (t )=0 t≤0
b)
para
para
para
f (t )=−7 3<t <10
f (t )=0 t≥10
f (t )=0 t≤3
f (t )=0 t≤0
f (t )=4 t >0 y t ≤5
f (t )=2 t >5 y t ≤10
f (t )=6 t >10