find L (cos³4t)? pls tell me the ans
Answers
Answer:
take it from brainy option of textbook
Answer:
. Find the Laplace transform of f(t)=e^{3t} using the definition of the Laplace transform. 2....
Question:
1. Find the Laplace transform of
f
(
t
)
=
e
3
t
using the definition of the Laplace transform.
2. Find
L
{
f
(
t
)
}
.
a.
f
(
t
)
=
3
t
2
−
5
t
+
7
b.
f
(
t
)
=
2
e
−
4
t
c.
f
(
t
)
=
3
c
o
s
2
t
−
s
i
n
5
t
d.
f
(
t
)
=
t
e
2
t
e.
f
(
t
)
=
e
−
t
s
i
n
3
t
Laplace Transform:
Given a function
f
(
t
)
defined for all real
t
⩾
0
,
then, the Laplace transform of
f
(
t
)
is a function of a new variable
s
given by
L
{
f
(
t
)
}
=
∞
∫
0
e
−
s
t
f
(
t
)
d
t
=
f
(
s
)
where
|
f
(
t
)
|
≤
M
e
a
t
i.e.
f
(
t
)
should be of exponential order and piece-wise continuous.
We use First Shifting Theorem of the Laplace transform in the given problem:
If
L
{
f
(
t
)
}
=
f
(
s
)
,
then
L
{
e
a
t
f
(
t
)
}
=
f
(
s
−
a
)
.
We also use following formulas of Laplace transforms in the given problem: