Lista 10 - Transformada de Laplace PDF

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Lista de exercícios sobre Transformada de Laplace...

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Cálculo III – Lista 10 – Transformada de Laplace 1) Use a Tabela de Transformadas de Laplace para encontrar a transformada F(s) das seguintes funções f(t). a) f ( t )  t  2e 3t b) f ( t ) 1  cosh (5t )

R: F(s) 

1 2  s2 s  3

1 s R: F(s)   2 s s  25 s2  8 s(s2  16)

c) f ( t ) cos2 (2 t )

R: F(s) 

d) f ( t ) (1  t )3

1 3 6 6 R: F(s)   2  3  4 s s s s

e) f ( t ) senh 2 (3t )

R: F(s)  s(s2

f) f (t ) et cos(t )

s1 R: F(s)  2 s  2s  2

g) f ( t )  t.e t

1 R: F(s)  (s  1) 2

h) f ( t ) senh (2 t )

R: F(s ) 

i) f ( t ) sen (2t )  cos (2 t )

R: F(s ) 

j) f (t ) e 10t

18  36)

2 s  4 2

2 s  2 s 4 s  4 2

R: F(s) 

1 s  10

2

k) f ( t )  t 2 .et f

R: F(s)  (s 1)3 

l) f (t ) e t .sen( t )

1 R: F(s)  2 s  2s  2

2) Encontre as Transformadas de Laplace inversa das funções F(s).

t3 2

a) F(s ) 

3 s4

R: f ( t) 

b) F(s) 

3 s 4

R: f ( t ) 3e 4t

c) F(s ) 

5  3s s2  9

R: f ( t ) 35 sen (3t )  3 cos(3t )

d) F(s) 

1 s5

R: f ( t ) e 5t

e) F(s ) 

9s 2 4 s

R: f ( t )  29 senh (2 t )  consh (2 t )

10s  3 25  s 2

R: f ( t )  10 cosh (5t )  53 senh (5t )

3s 1 s2  4

R: f ( t ) 3 cos ( 2t )  21 sen ( 2t )

3 s2  4

R: f ( t )  32 sen (2 t )

f) F(s ) 

g) F(s ) 

h) F(s) 

4

i) F(s)  (s 1)3 

R: f ( t )  2 t 2 et

j) F(s ) 

2s  3 s2  4

R: f ( t ) 2 cosh ( 2t ) 

k) F(s ) 

2 s2  3s  4

R: f ( t)  25 et 

2 5

e 4t

3 senh (2 t ) 2...