a. First, compute the Laplace transform of f(t). -2s -6s L{f(t)}(s) = b. Next, take the Laplace transform of the left-hand-side of the differential equation, set it equal to your answer from Part a. and solve for L { -2s -6s -e -6s – 58 L {y(t)}(s) = + s(s? + 10s+ 29) s2 + 10s + 29 c. We will need to take the inverse Laplace transform in order to find y(t). To do so, let's first rewrite L {y(t)} as L {u(?}{(+) = ( - F(s) 1 -28 e e - F(s) - 6F(s) + 2G(s) 1 -6s 29 where s+10 F(s) = and G(s) = s2 + 10s + 29 s2 + 10s + 29 d. Part c. indicates we will need L-1{F(s)} and L-1{G(s)}. Let's go ahead and find those now. L-'{F(s)}(t) = and L-1{G(s)}(t) e. Use your answer in Part d. to compute L-1{e=2*F(s)} and L-1 {e-6*F(s)}. L-'{e-»F(s)}(t) = and C-1{e-6*F(s)}(t) = f. Finally, combine all the previous steps to write down y(t).

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
icon
Related questions
Question

Parts d through f.

In the following parts, use h(t – c) for the Heaviside function he(t) when necess
essary.
a. First, compute the Laplace transform of f(t).
-2.s
e
-6s
e
L{f(t)}(s) =
S
S
b. Next, take the Laplace transform of the left-hand-side of the differential equation, set it equal to your answer from Part a. and solve for L {y(t)}.
-6s
-2s
- e
-6s – 58
L {y(t)}(s) =
s(s- + 10s +
29)
2.
s + 10s +29
c. We will need to take the inverse Laplace transform in order to find y(t). To do so, let's first rewrite L{y(t)} as
1
1
-2s
e
1
L {y(t)}(s)
F(s))
6s
e
F(s)
- 6F(s) + 2G(s)
-
-
-
29
S
29
S
where
s+ 10
1
F(s) =
and G(s) =
s + 10s + 29
+ 10s + 29
d. Part c. indicates we will need L-1{F(s)} and L-1{G(s)}. Let's go ahead and find those now.
L-1{F(s)}(t) =
and
L-' {G(s)}(t)
e. Use {e¯6*F(s)}.
your answer in Part d. to compute L-1 {e¯2$F(s)} and L-1
L-'{e-2"F(s)}(t) =
and L-1{e-6*F(s)}(t) =
-6s F(s)}(t)
1
f. Finally, combine all the previous steps to write down y(t).
Transcribed Image Text:In the following parts, use h(t – c) for the Heaviside function he(t) when necess essary. a. First, compute the Laplace transform of f(t). -2.s e -6s e L{f(t)}(s) = S S b. Next, take the Laplace transform of the left-hand-side of the differential equation, set it equal to your answer from Part a. and solve for L {y(t)}. -6s -2s - e -6s – 58 L {y(t)}(s) = s(s- + 10s + 29) 2. s + 10s +29 c. We will need to take the inverse Laplace transform in order to find y(t). To do so, let's first rewrite L{y(t)} as 1 1 -2s e 1 L {y(t)}(s) F(s)) 6s e F(s) - 6F(s) + 2G(s) - - - 29 S 29 S where s+ 10 1 F(s) = and G(s) = s + 10s + 29 + 10s + 29 d. Part c. indicates we will need L-1{F(s)} and L-1{G(s)}. Let's go ahead and find those now. L-1{F(s)}(t) = and L-' {G(s)}(t) e. Use {e¯6*F(s)}. your answer in Part d. to compute L-1 {e¯2$F(s)} and L-1 L-'{e-2"F(s)}(t) = and L-1{e-6*F(s)}(t) = -6s F(s)}(t) 1 f. Finally, combine all the previous steps to write down y(t).
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Inductor
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,