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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT
![Given that, flt) = 3 tv - 4 Sin (54)
we have to determine
of f(t).
We know that
where F(S) = 2√ {f(t)}.
in dn
4 { +^+1+1} = (-1)" d² [ F10]
we know that ↳ { Sincatl} = a ar
Again
а
Šta
L {e^² + f(t)} = F(S-a) where F(S) = 2 {f(t)}
L {f(t)} i.e. Laplace transformation
=
. Now, flt) = 3+²-4 Sin (5+)
2². W { f(t)} = 2 { 3+²-4 Sin(st)}
L
JI
-
11
= 3 4 5 (- ==- ) -
ds
= 3x -
L {3+~} - [{ 4 Sin (5+)}
3 ⋅ (-1) 1/2²/24 (-1/2) - 4. 5
_. & {f(+)} =
2
(5-3)3
3x-2²7
S3
:. 4 { @²+ + ² }
...
e
6
$3
-
او
53
20
5+25
ww/ro
and
20
5+25
Now, w{tr} = Hiju da 2 (3)
L
d2
वडर
ds (sv)
3t
Therefore { e³² tv} =
[2√ e³t+~}
4x5
5+25
20
5+25
5+5²
2
(5-3)³](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3a58f98-b5c9-44bb-9235-4b412fc4242f%2F2239cb06-709e-4cb0-8af9-485a52a0dc04%2F7dphm2t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given that, flt) = 3 tv - 4 Sin (54)
we have to determine
of f(t).
We know that
where F(S) = 2√ {f(t)}.
in dn
4 { +^+1+1} = (-1)" d² [ F10]
we know that ↳ { Sincatl} = a ar
Again
а
Šta
L {e^² + f(t)} = F(S-a) where F(S) = 2 {f(t)}
L {f(t)} i.e. Laplace transformation
=
. Now, flt) = 3+²-4 Sin (5+)
2². W { f(t)} = 2 { 3+²-4 Sin(st)}
L
JI
-
11
= 3 4 5 (- ==- ) -
ds
= 3x -
L {3+~} - [{ 4 Sin (5+)}
3 ⋅ (-1) 1/2²/24 (-1/2) - 4. 5
_. & {f(+)} =
2
(5-3)3
3x-2²7
S3
:. 4 { @²+ + ² }
...
e
6
$3
-
او
53
20
5+25
ww/ro
and
20
5+25
Now, w{tr} = Hiju da 2 (3)
L
d2
वडर
ds (sv)
3t
Therefore { e³² tv} =
[2√ e³t+~}
4x5
5+25
20
5+25
5+5²
2
(5-3)³
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