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: 9 s 2 − 12 s + 28 s ( s 2 + 4 ) TABLE 5. 3. 1 Elementary Laplace transforms. f ( t ) = L − 1 { F ( s ) } F ( s ) = L { f ( t ) } 1 1 s , s > a sin a t a s 2 + a 2 , s > a cos a t s s 2 + a 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: 9 s 2 − 12 s + 28 s ( s 2 + 4 ) TABLE 5. 3. 1 Elementary Laplace transforms. f ( t ) = L − 1 { F ( s ) } F ( s ) = L { f ( t ) } 1 1 s , s > a sin a t a s 2 + a 2 , s > a cos a t s s 2 + a 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:
9
s
2
−
12
s
+
28
s
(
s
2
+
4
)
TABLE 5. 3. 1
Elementary Laplace transforms.
f
(
t
)
=
L
−
1
{
F
(
s
)
}
F
(
s
)
=
L
{
f
(
t
)
}
1
1
s
,
s
>
a
sin
a
t
a
s
2
+
a
2
,
s
>
a
cos
a
t
s
s
2
+
a
2
,
s
>
a
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