Concept explainers
(a)
Find the inverse Laplace transform for the given function
(a)
Answer to Problem 30E
The inverse Laplace transform for the given function is
Explanation of Solution
Given data:
Consider the Laplace transform function is,
Formula used:
Write the general expression for the inverse Laplace transform.
Calculation:
The equation (1) can be rewritten as follows,
Expand
Here,
A and B are the constants.
Find the constants by using algebraic method.
Consider the partial fraction,
Equating the coefficients of
Equating the coefficients of constant term in equation (5).
Substitute equation (6) in equation (7) to find the constant B.
Substitute 1 for B in equation (6) to find the constant A.
Substitute
Apply inverse Laplace transform of equation (2) in equation (8).
Write the general expression to find the inverse Laplace transform function.
Apply inverse Laplace transform function of equation (10) in equation (9).
Conclusion:
Thus, the inverse Laplace transform for the given function is
(b)
Find the inverse Laplace transform for the given function
(b)
Answer to Problem 30E
The inverse Laplace transform for the given function is
Explanation of Solution
Given data:
Consider the Laplace transform function is,
Calculation:
The equation (11) can be rewritten as follows,
Expand
Here,
A, B, C are the constants.
Find the constants by using algebraic method.
Consider the partial fraction,
Equating the coefficients of constant term in equation (14).
Equating the coefficients of
Equating the coefficients of
Substitute equation (15) in equation (16),
Substitute
Substitute
Substitute
Apply inverse Laplace transform of equation (2) in equation (8).
Apply inverse Laplace transform function of equation (10) in equation (18).
Conclusion:
Thus, the inverse Laplace transform for the given function is
(c)
Find the inverse Laplace transform for the given function
(c)
Answer to Problem 30E
The inverse Laplace transform for the given function is
Explanation of Solution
Given data:
Consider the Laplace transform function is,
Calculation:
Expand
Here,
A, B, C, and D are the constants.
Find the constants by using algebraic method.
Consider the partial fraction,
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Apply inverse Laplace transform of equation (2) in equation (8).
Apply inverse Laplace transform function of equation (10) in equation (22).
Conclusion:
Thus, the inverse Laplace transform for the given function is
(d)
Verify the functions given in Part (a), Part (b), and Part (c) with MATLAB.
(d)
Answer to Problem 30E
The given functions are verified with MATLAB.
Explanation of Solution
Calculation:
Consider the function given in Part (a).
The MATLAB code for the given function:
syms s t
ilaplace (1/(s*s + 9*s + 20))
MATLAB output:
Consider the function given in Part (b).
The MATLAB code for the given function:
syms s t
ilaplace((4/(s*s*s + 18*s*s + 17*s)))
MATLAB output:
Consider the function given in Part (c).
The MATLAB code for the given function:
syms s t
ilaplace(3/s/(s+1)/(s+4)/(s+5)/(s+2))
MATLAB output:
Conclusion:
Thus, the given functions are verified with MATLAB.
Want to see more full solutions like this?
Chapter 14 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
- 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)arrow_forwardFind the Inverse Laplace Transform of the following: 4. F(s) = 5. F(s) = 1 √2s+3 e4-3s (s+4)5/2arrow_forward(8) Using the method that applies the Laplace Transform to the circuit below. Find v(t) for t20. Find i1(t) 10k 20 i, a b V + 30 V t = 0 500 mH S100 100 20k 1/3 mFarrow_forward
- Apply the initial- and final-value theorems to each transform pair . 1. F(s)=280s2+14s+245. 2. F(s)=−s2+52s+445s(s2+10s+89). 3. F(s)=14s2+56s+152(s+6)(s2+4s+20). 4. F(s)=8(s+1)2(s2+10s+34)(s2+8s+20).arrow_forwardI. Inverse Laplace Transform. 1. F(s) = (6s+6) (s²+s+1) (16s+48) 2. F(s) = (4s²+4s-3)arrow_forwardQ13 The Laplace Transform of f(t) = e²"sin (5t) u (t) is (B) 5 (A) s – 4s+ 29 s+5 5 8 - 2 (C) 2 – 4s+ 29 (D) s+5 -arrow_forward
- Laplace transform F(s) of the following signal sin4(t-1)*u(t-1) O a. F(s) is a function of "s" Only O b. None of the answers F(s) is a function of "s^2" Only F(s) is a function of "s" and "s^2" O c. O d.arrow_forward1. Find the inverse Laplace transform of the following transforms. 3s+17 (a) F(s) : s(s+2)(s+7) s+11 (b) F (s) %D s2 (s+3)2 s+17 (c) F(s) = (s+5)2(s+8) 2s+27 (d) F (s) = (s²+5)(s² +9s+20)arrow_forwardQuestion The Laplace transform of f (t) = 5 cos(7t)- 7e2t +t³ is: 5s F(s) , * 2 6. F(s) = s2+4 S-2 s+3 This option O This option 7 F(s) = +: 4. F(s) $2+49 S-2 s2+4 s+3 This option This optionarrow_forward
- Find the inverse Laplace transform of 5. F(s)= s(s²+2s+ 5)arrow_forwardFind the inverse Laplace transform of s* + 2s3 + 3s? + 4s + 5 F(s) s(s + 1)arrow_forwardSolving Differential Equation using Laplace transform: dy(t)/dt +2y(t)=3u(t) Initial condition y(0) = 0 Hello, I am doing some practice and I want to make sure I am doing this right while using the correct steps. Thank you for your time and help.arrow_forward
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,