Concept explainers
(a)
Find the inverse Laplace transform for the given function
(a)
Answer to Problem 32P
The inverse Laplace transform for the given function is
Explanation of Solution
Given data:
The Laplace transform function is ,
Formula used:
Write the general expression for the inverse Laplace transform.
Write the general expression to find the inverse Laplace transform function.
Here,
Calculation:
Consider the given function,
Expand
Here,
A, B, and C are the constants.
Now, to find the constants by using residue method.
Constant A:
Substitute equation (5) in equation (7) to find the constant A.
Constant B:
Substitute equation (5) in equation (8) to find the constant B.
Constant C:
Substitute equation (5) in equation (9) to find the constant C.
Substitute
Substitute
Apply inverse Laplace transform function given in equation (3) and (4) to equation (8).
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 32P
The inverse Laplace transform for the given function is
Explanation of Solution
Given data:
The Laplace transform function is,
Formula used:
Write the general expression for the inverse Laplace transform.
Write the general expressions to find the inverse Laplace transform function.
Calculation:
Consider the given function,
Expand
Here,
D, E, and F are the constants.
Now, to find the constants by using residue method.
Constant D:
Substitute equation (13) in equation (15) to find the constant D.
Constant E:
Substitute equation (13) in equation (16) to find the constant E.
Constant F:
Substitute equation (13) in equation (17) to find the constant F.
Reduce the equation as follows,
Substitute
Substitute
Apply inverse Laplace transform function given in equation (3) and (12) to 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 32P
The inverse Laplace transform for the given function is
Explanation of Solution
Given data:
The Laplace transform function is,
Formula used:
Write the general expression for the inverse Laplace transform.
Write the general expressions to find the inverse Laplace transform function.
Calculation:
Consider the given function,
Expand
Here,
A, B, and C are the constants.
Now, to find the constants by using algebraic method.
Consider the partial fraction,
Reduce the equation as follows,
Equating the coefficients of
Equating the coefficients of
Equating the coefficients of constant term in equation (23).
Substitute equation (24) in equation (25).
Substitute the equation (27) in equation (26) to find the constant A.
Substitute 5 for A in equation (24) to find the constant B.
Substitute 5 for A in equation (27) to find the constant C.
Substitute
Substitute
Apply inverse Laplace transform function given in equation (3) and (20) to equation (29).
Conclusion:
Thus, the inverse Laplace transform for the given function is
Want to see more full solutions like this?
Chapter 15 Solutions
Fundamentals Of Elec...-connect Access
- A system with an impulse response of h(t) = e(-t/2) is driven by a forcing function x(t)=1-u(t-1). Determine the time domain output response y(t) using: a) Time-domain convolutional integral b) The Laplace transform and the inverse Laplace transformarrow_forwardConsider a Laplace transform F(s) = 2(s + 1)/(s^2 + 4s + 7). Determine the initial value and final value of f(t).arrow_forwardDetermine the inverse laplace transform of the following: a. 1/[(s-2)^2 + 9] b. s(s^2 - 9)/(s^2 +9)^2arrow_forward
- find the inverse laplace transform for x(s)=2s+100/(s+1)(s+8)(s+10)arrow_forwardDetermine the Inverse Laplace Transform of the following: 1.) 1/[s(s²-1)] 2.) (s²+7s-1)/[(s-2)(s²+4)]arrow_forwardFind the Laplace transform of each of the following functions: 1. f(t) = 20e−500(t−10)u(t−10). 2. f(t)=(5t+20)[u(t+4)−u(t+2)]−5t[u(t+2)−u(t−2)]+(5t−20)[u(t−2)−u(t −4)].arrow_forward
- The Transfer Function given below; a) Find the zeros and polarities. b) Indicate whether it is stable or not. c) Find the function y(t) (the inverse Laplace transform).arrow_forwardConsider the function, F(s)= 5/s(s2+3s+2) where F(s) is the Laplace transform of the function f(t). The initial value of f(t) will be ?arrow_forwardConsider the function, F(s) = 5/s(s2+3s+2) where F(s) is the Laplace transform of the function f(t). The initial value of f(t) is equal to ?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,