Exercícios_Transformada_Laplace1

Prévia do material em texto

Exercícios de Aplicação das Propriedades da Transformada de Laplace 
 
Determinar a Transformada de Laplace das Funções (Alguns exercícios podem 
ser resolvidos de várias formas. Tente mais de uma para praticar). 
 
1. f(t) = 3t 
2. f(t) = 5 cos2t 
3. ( ) t2ettf −+= 
4. ( ) te5t10sen32tf −−+= 
5. ( ) ( ) ( )3tu3t2costf −−= 
6. ( ) ( )2tuttf −= 
7. ( ) ( )1tuetf t3 −= − 
8. ( ) ( )3tut2costf −= 
9. ( ) tetf t2 = − 
10. ( ) ( )tutetf t2 = − 
11. ( ) t2cosetf t = − 
12. ( ) tcostetf t = − 
13. ( ) ( )tutcostetf t = − 
14. ( ) tcost3coste8tf t2 = − 
15. ( ) ( ) ( )2tu4t2sen4tf 2 −−= 
 
 
Resolver também os exercícios do livro texto 4ª Ed.: 
Pag. 694 - E16.4 a E16.9 
Pág 711 – 16.2 a 16.10 
 
 
 
 
 
Respostas 
 
1. ( )
2s
3
sF 
2. ( )
4s
s5
sF
2 +
= 
3. ( )
2s
1
s
1
sF
2 +
+= 
4. ( )
1s
5
100s
30
s
2
sF
2 +
−
+
+= 
5. ( ) 





+
= −
4s
s
esF
2
s3 
6. ( ) 





+= −
s
2
s
1
esF
2
s2 
7. ( )
( )
( )3s
e
sF
3s
+
=
+−
 
8. ( )












+
−





+
= −
4s
2
6sen
4s
s
6cosesF
22
s3 
9. ( )
( )22s
1
sF
+
= 
10. ( )
( )22s
1
sF
+
= 
11. ( )
( ) 41s
1s
sF
2
++
+
= 
12. ( )
( )
( ) 22
2
11s
11s
sF
++
−+
= 
13. ( )
( )
( ) 22
2
11s
11s
sF
++
−+
= 
14. ( )
( )
( ) 
( )
( )  







++
−+
+
++
−+
=
22
2
22
2
162s
162s
42s
42s
4sF 
15. ( ) s2
2
e
16s
s
s
1
2sF −






+
−= 
 
 
 
 
 
 
 
 
Exercícios do Livro, pág. 711 
 
2. ( ) 





+
=
−
1s
1
x4
e
sF
a
 
3. ( )
22
2
2
2
as
sa
as
a
s
a
s
a
sF
+
+
+
++= 
4. ( )
( )
( )
( ) ++
++
=
+−
senascos
as
e
sF
22
as
 
5. ( ) ( )
( ) 







+
+
+
= +−
as
4
as
1
esF
2
as4 
6. ( )
( )
as
e
sF
as
+
=
+−
 
7. ( ) ( )
( ) 







+
+
+
= +−
as
1
as
1
esF
2
as 
8. ( ) 







+
+= −
1s
1
s
1
esF
2
s 
9. ( ) 





+
−
+
= −
2s
1
1s
1
esF s2 
 
10. 
( )
















+

−








+
+
−
+
=
−
sen
s
s2
coss
s
s
s
e
sF
2222
22
22
s