(d) f"(t) – 4f(t) = sin 2t where f(0) = 1 and f'(0) = -2 Taking Laplace transforms of both sides of the equati L{f"(t)} – L{4f(t)} = L{sin 2t} | %3D so that [s F(s) – sf (0) – f'(0)] – 4F(s) =- s2 + 22 That is (s2 – 4)F(s) – s,1 – (-2) = %3D s2 + 22 S-2 it. 2 so F(s) = (s2 – 4)(s² + 2²) – 4 1 1 1 16 s+ 2 15 1 %3D 16 s - 2 8 s2 +22
(d) f"(t) – 4f(t) = sin 2t where f(0) = 1 and f'(0) = -2 Taking Laplace transforms of both sides of the equati L{f"(t)} – L{4f(t)} = L{sin 2t} | %3D so that [s F(s) – sf (0) – f'(0)] – 4F(s) =- s2 + 22 That is (s2 – 4)F(s) – s,1 – (-2) = %3D s2 + 22 S-2 it. 2 so F(s) = (s2 – 4)(s² + 2²) – 4 1 1 1 16 s+ 2 15 1 %3D 16 s - 2 8 s2 +22
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(d) f"(t) – 4f(t) = sin 2t where f(0) = 1 and f'(0) = -2
Taking Laplace transforms of both sides of the equati
L{f"(t)} – L{4f(t)} = L{sin 2t}
so that [s F(s) – sf (0) – f'(0)] – 4F(s) =-
s2 + 22
That is (s2 – 4)F(s) – s,1 – (-2) =
s2 + 22
2
S-2
so F(s) =
(s2 – 4)(s² + 2²) – 4
-
1 1 1
16 s+ 2
15
1
16 s - 2 8 s2 +22](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0133bc0-1058-4b15-a09f-36917b166219%2F67ea3b52-9276-4820-bf49-861341804984%2Fw5ddob_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(d) f"(t) – 4f(t) = sin 2t where f(0) = 1 and f'(0) = -2
Taking Laplace transforms of both sides of the equati
L{f"(t)} – L{4f(t)} = L{sin 2t}
so that [s F(s) – sf (0) – f'(0)] – 4F(s) =-
s2 + 22
That is (s2 – 4)F(s) – s,1 – (-2) =
s2 + 22
2
S-2
so F(s) =
(s2 – 4)(s² + 2²) – 4
-
1 1 1
16 s+ 2
15
1
16 s - 2 8 s2 +22
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)