Question

t cos at laplace transform​

Answer 1

A Laplace transform converts a function of
t
,
f
(
t
)
, into a new function of
s
,
F
(
s
)
. We denote that as:
L
[
f
(
t
)
]
=
F
(
s
)
where the actual transform can be acquired from a table of Laplace transforms.
For
f
(
t
)
=
t
cos
(
a
t
)
:
L
[
f
(
t
)
]
=
L
[
t
cos
(
a
t
)
]
=
s
2
−
a
2
(
s
2
+
a
2
)
2
Therefore, for your function, plug in
a
=
1
to get:
L
[
f
(
t
)
]
=
L
[
t
cos
t
]
=
s
2
−
1
2
(
s
2
+
1
2
)
2
=
s
2
−
1
(
s
2
+
1
)
2

Answer 2

Answer:

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