Subido por edwin vargas

# Tabla transformada de Laplace

Anuncio
```38
Modeling and Analysis of Dynamic Systems
TABLE 2.2
Laplace Transform Pairs
f(t)
F(s)
1
2
Unit impulse δ(t)
1, Unit step us(t)
3
t, Unit ramp ur(t)
1
1
s
1
s2
4
5
6
7
δ(t − a)
u(t − a)
tn – 1, n = 1,2,3, …
ta – 1, a &gt; 0
8
e−at
9
te−at
1
(s + a) 2
10
tne−at, n = 1, 2, 3, …
n!
(s + a)n +1
11
1
(e − at − e − bt ) , a ≠ b
b−a
1
(s + a)(s + b)
12
1
(ae − at − be − bt ) , a ≠ b
a−b
s
(s + a)(s + b)
13
1 
1

(be − at − ae − bt )
1+
ab  a − b

1
s(s + a)(s + b)
14
1
(−1 + at + e − at )
a2
1
s 2 (s + a)
15
1
(1 − e − at − ate − at )
a2
1
s (s + a) 2
16
sinωt
17
cosωt
18
e−σt sinωt
19
e−σt cosωt
s+σ
(s + σ ) 2 + ω 2
20
1 − cosωt
ω2
s (s + ω 2 )
21
ωt − sinωt
ω3
s (s 2 + ω 2 )
22
t cosωt
s2 − ω 2
(s 2 + ω 2 ) 2
23
1
t sinωt
2ω
s
(s 2 + ω 2 ) 2
No.
e–as
e–as/s
(n − 1)!/sn
Γ(a)/sa
1
s+a
ω
s2 + ω 2
s
s2 + ω2
ω
(s + σ ) 2 + ω 2
2
2
(continued)
39
Complex Analysis, Differential Equations, and Laplace Transformation
TABLE 2.2 (Continued)
Laplace Transform Pairs
f(t)
F(s)
24
1
(sin ωt − ωt cos ωt )
2ω 3
1
(s 2 + ω 2 ) 2
25
1
(sin ωt + ωt cos ωt )
2ω
s2
(s 2 + ω 2 ) 2
26
1
1
1

sin ω 2t −
sin ω1t , ω12 ≠ ω 22
ω1
ω − ω12 ω 2

1
(s 2 + ω12 )(s 2 + ω 22 )
27
1
(cos ω1t − cos ω 2t ), ω12 ≠ ω 22
ω 22 − ω12
s
(s 2 + ω12 )(s 2 + ω 22 )
28
sinh at
a
s2 − a2
29
cosh at
s
s2 − a2
30
1 1
1

sinh at − sinh bt , a ≠ b
b
a 2 − b 2 a

1
(s 2 − a 2 )(s 2 − b 2 )
31
1
[cosh at − cosh bt ], a ≠ b
a2 − b2
s
(s 2 − a 2 )(s 2 − b 2 )
32
1
 3
at
1  − at
1 
at − π
e + 2e 2 sin 
2
6 
3a 2 
1
s 3 + a3
33
1
 3
at
1  − at
1 
at + π
−e + 2e 2 sin 
3a 
2
6 
s
s 3 + a3
34
1
 3
− at
1  − at
1 
e + 2e 2 sin 
at + π
2 
2
6 
3a 
1
s 3 − a3
35
1
 3
− at
1  − at
1 
at − π
e + 2e 2 sin 
3a 
2
6 
s
s 3 − a3
36
1
[cosh at sin at − sinh at cos at ]
4a3
1
s 4 + 4a 4
37
1
sinh at sin at
2a 2
s
s 4 + 4a 4
38
1
(sinh at − sin at )
2a 3
1
s4 − a4
39
1
(cosh at − cos at )
2a 2
s
s4 − a4
No.
2
2
```