Question

Laplace transform of f(2t) is equal to​

Answer 1

Here is an approach.

(sin2)=22+22=22+4
L
(
sin
⁡
2
t
)
=
2
s
2
+
2
2
=
2
s
2
+
4
, using the table.
(−sin2)=2(+1)2+4
L
(
e
−
t
sin
⁡
2
t
)
=
2
(
s
+
1
)
2
+
4
, using frequency shifting.
(−sin2)=−(2(+1)2+4)=4(+1)((+1)2+4)2
L
(
t
e
−
t
sin
⁡
2
t
)
=
−
d
d
s
(
2
(
s
+
1
)
2
+
4
)
=
4
(
s
+
1
)
(
(
s
+
1
)
2
+
4
)
2
, using frequency differentiation.