In each of Problems 9 through 24, using the linearity of L − 1 , partial fraction expansions, and Table 5.3.1 to find the inverse Laplace transform of the given function: 12 s 2 − 7 s + 28 ( s 2 − 8 s + 25 ) ( s + 3 ) TABLE 5. 3. 1 Elementary Laplace transforms. f ( t ) = L − 1 { F ( s ) } F ( s ) = L { f ( t ) } e a t 1 s − a , s > a e a t sin b t b ( s − a ) 2 + b 2 , s > a
In each of Problems 9 through 24, using the linearity of L − 1 , partial fraction expansions, and Table 5.3.1 to find the inverse Laplace transform of the given function: 12 s 2 − 7 s + 28 ( s 2 − 8 s + 25 ) ( s + 3 ) TABLE 5. 3. 1 Elementary Laplace transforms. f ( t ) = L − 1 { F ( s ) } F ( s ) = L { f ( t ) } e a t 1 s − a , s > a e a t sin b t b ( s − a ) 2 + b 2 , s > a
In each of Problems 9 through 24, using the linearity of
L
−
1
, partial fraction expansions, and Table 5.3.1 to find the inverse Laplace transform of the given function:
12
s
2
−
7
s
+
28
(
s
2
−
8
s
+
25
)
(
s
+
3
)
TABLE 5. 3. 1
Elementary Laplace transforms.
f
(
t
)
=
L
−
1
{
F
(
s
)
}
F
(
s
)
=
L
{
f
(
t
)
}
e
a
t
1
s
−
a
,
s
>
a
e
a
t
sin
b
t
b
(
s
−
a
)
2
+
b
2
,
s
>
a
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