Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Chapter 15, Problem 50P
To determine
Find the time-varying function
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Express the function below using window and step functions and compute its Laplace transform.
2190
Q
0-
5x
16
Click here to view the table of Laplace transforms.
Click here to view the table of properties of Laplace transforms.
Express g(t) using window and step functions. Choose the correct answer below.
A. g(t)= (sin 8t)u t--
(sin 8t)u (1-56)
OB. 9(t)=11
sin (81)
OC, 9(t) = (sin 8t)II
5x (t) + (sin 8t)u t-
0.7 16
salt)
0.16
I
OD. g(t)=(cos 8t)u t--
: 8tu (1-556)
16
Compute the Laplace transform of g(t).
L(g) =
(Type an expression using s as the variable.)
Answer All of the Questions Below
1.
Find the inverse Laplace Transform of the following function below.
i. F(s) =
s+ 5
s? + 8s + 65
ix. F(s) =
49
7s + 21
ii. F(s)
5s? + 14s + 2
(s-2)(s+4)?
%3D
X. F(s) =
3s
(s+3)² + 64
iii. F(s)
3s + 4
s? + 16
%3D
2s - 3
2s2 - 8s + 16
xi. F(s) =
iv. F(s) = _ 5s² + 14s + 2
(s-2) (s+3)?
xii. F(s) =,
s? + 12
s (s+1)(s+3)
v. F(s) =.
s + 5
(s+3) + 9
%3D
10s? + 4
s (s+1)(s+2)²
xii. F(s) =
vi. F(s)
8s + 2
s? + 3s + 2
xiii. F(s) =
1
s (s? + 6s + 9)
vii. F(s)
= s? + 3s + 1
(s? + s)
xiv. F(s) =
3s + 2
s? + 3s + 2
viii. F(s)
8(s + 2)
(s+1)(s+3)(s+5)
Problem2. Find i (t) for t > 0 in the following circuit. Use differential equation approach
this problem. Don't use Laplace transform theory.
402
Ri(t)
+12 V
1H
2₂ 202
#
0.5 F
Uc (t)
t = 0
Chapter 15 Solutions
Fundamentals of Electric Circuits
Ch. 15.2 - Prob. 1PPCh. 15.2 - Prob. 2PPCh. 15.3 - Prob. 3PPCh. 15.3 - Prob. 4PPCh. 15.3 - Prob. 5PPCh. 15.3 - Prob. 6PPCh. 15.3 - Obtain the initial and the final values of...Ch. 15.4 - Prob. 8PPCh. 15.4 - Find f(t) if F(s)=48(s+2)(s+1)(s+3)(s+4)Ch. 15.4 - Obtain g(t) if G(s)=s3+2s+6s(s+1)2(s+3)
Ch. 15.4 - Find g(t) given that G(s)=20(s+1)(s2+4s+13)Ch. 15.5 - Graphically convolve the two functions in Fig....Ch. 15.5 - Given g(t) and f(t) in Fig. 15.20, graphically...Ch. 15.5 - Use convolution to find vo(t) in the circuit of...Ch. 15.6 - Prob. 15PPCh. 15.6 - Prob. 16PPCh. 15 - Prob. 1RQCh. 15 - Prob. 2RQCh. 15 - Prob. 3RQCh. 15 - Prob. 4RQCh. 15 - Prob. 5RQCh. 15 - If F(s) = 1/(s + 2), then f(t) is (a) e2t u(t) (b)...Ch. 15 - Prob. 7RQCh. 15 - Prob. 8RQCh. 15 - Prob. 9RQCh. 15 - Prob. 10RQCh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Find F(s) if: (a) ft=6etcosh2t (b) ft=3te2tsinh4t...Ch. 15 - If g(t) = 4e 2t cos 4t, find G(s).Ch. 15 - Prob. 13PCh. 15 - Prob. 14PCh. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Design a problem to help other students better...Ch. 15 - Let F(s)=18(s+1)(s+2)(s+3) (a) Use the initial and...Ch. 15 - Determine the initial and final values of f(t), if...Ch. 15 - Prob. 27PCh. 15 - Prob. 28PCh. 15 - Prob. 29PCh. 15 - Prob. 30PCh. 15 - Find f(t) for each F(s): (a) 10ss+1s+2s+3 (b)...Ch. 15 - Prob. 32PCh. 15 - Prob. 33PCh. 15 - Prob. 34PCh. 15 - Obtain f(t) for the following transforms: (a)...Ch. 15 - Prob. 36PCh. 15 - Prob. 37PCh. 15 - Prob. 38PCh. 15 - Determine f(t) if: (a)...Ch. 15 - Show that...Ch. 15 - Prob. 41PCh. 15 - Design a problem to help other students better...Ch. 15 - Prob. 43PCh. 15 - Prob. 44PCh. 15 - Given h(t) = 4e2tu(t) and x(t) = (t) 2e 2tu(t),...Ch. 15 - Given the following functions...Ch. 15 - A system has the transfer function...Ch. 15 - Find f(t) using convolution given that: (a)...Ch. 15 - Prob. 49PCh. 15 - Prob. 50PCh. 15 - Given that v(0) = 5 and dv(0)/dt = 10, solve...Ch. 15 - Prob. 52PCh. 15 - Prob. 53PCh. 15 - Design a problem to help other students better...Ch. 15 - Prob. 55PCh. 15 - Solve for v(t) in the integrodifferential equation...Ch. 15 - Prob. 57PCh. 15 - Given that dvdt+2v+50tv()d=4u(t) with v(0) = 1,...Ch. 15 - Solve the integrodifferential equation...Ch. 15 - Prob. 60P
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- Find the Laplace transforms of the following time functions. you can use the Laplace Transform Tables. f(t) = sin(2t) + 2 cos(2t) + et sin(2t)arrow_forwardFind the Laplace Transform of the following. Answers must be in a simplified form and solutions must be shown completely. 3. t cos (t)dtarrow_forward2(s+9) The Inverse Laplace Transform of is: s2+2s+50 Select one: O a. 3.03e-tcos (7t – 48.7)u(t) O b. 3.03e-tsin (7t + 48.7°)u(t) Oc. 6.06e-tcos (7t + 56.3°)u(t) O d. 3.03e-tcos (7t + 48.7°)u(t) O e. 3.03e-tsin (7t – 48.7°)u(t)arrow_forward
- i. Determine from first principles the Laplace Transform of t+2e=t -6s+85-56 ii. Show that f (t) = {4sin (2t) – 6e“} =F+4)(3-4)arrow_forwardDetermine the z transform ofthe following n+3 xn) = n3) U (n+3) %3Darrow_forwardThe Laplace transform of the following function is: f(t) = 8u(t-1) + 2u(t − 5) – u(t) - Select one: a. F(s) = §els b. O ○ c. F(s) = F(s) = O d. F(s) = = els es 90/0000100 e - - + / e-8 2 - e+e- ³ + 3/2e - 1 8² e + ²/e-58-1 8 Sarrow_forward
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