Concept explainers
(a)
Find the inverse Laplace transform for the given function
(a)
Answer to Problem 36P
The inverse Laplace transform
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:
Expand
Here,
A, B, C, and D are the constants.
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
Equating the coefficients of constant term in equation (7) to find the constant B.
Substitute equation (11) in equation (10) to find the constant A.
Substitute equation (12) in equation (8).
Substitute equation (11), (12), and (13) in equation (9).
Substitute equation (14) in equation (13).
Substitute equation (11), (12), (14) and (15) in equation (6) to find
Apply inverse Laplace transform of equation (2) in equation (16).
Apply inverse Laplace transform function of equation (3), (4), (5) in equation (17).
Conclusion:
Thus, the inverse Laplace transform
(b)
Find the inverse Laplace transform for the given function
(b)
Answer to Problem 36P
The inverse Laplace transform
Explanation of Solution
Given data:
The Laplace transform function is,
Calculation:
Expand
Here,
A, B, and C are the constants.
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 (20) to find the constant A.
Substitute equation (23) in equation (21) to find the constant B.
Substitute equation (23) and (24) in equation (22).
Substitute equation (23), (24), and (25) in equation (19) to find
Apply inverse Laplace transform of equation (2) in equation (26).
Apply inverse Laplace transform function of equation (3), (4), (5) in equation (27).
Conclusion:
Thus, the inverse Laplace transform
(c)
Find the inverse Laplace transform for the given function
(c)
Answer to Problem 36P
The inverse Laplace transform
Explanation of Solution
Given data:
Consider the Laplace transform function is,
Formula used:
Write the general expression to find the inverse Laplace transform function.
Calculation:
Expand
Here,
A, B, C, and D are the constants.
Find the constants by using algebraic method.
Consider the partial fraction,
Reduce the equation as follows,
Equating the coefficients of constant term in equation (32) to find the constant A.
Equating the coefficients of
Equating the coefficients of
Equating the coefficients of
Substitute equation (33) in equation (36).
Substitute equation (33) in equation (34).
Substitute equation (33), (37) and (38) in equation (35).
Substitute equation (38) in equation (39).
Reduce the equation as follows,
Substitute equation (40) in equation (38) to find the constant B.
Substitute equation (41) in equation (37) to find the constant D.
Substitute equation (33),(40), (41), and (42) in equation (31) to find
Reduce the equation as follows,
Apply inverse Laplace transform of equation (2) in equation (43).
Apply inverse Laplace transform function of equation (3), (19) in equation (44).
Conclusion:
Thus, the inverse Laplace transform
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Chapter 15 Solutions
Fundamentals of Electric Circuits
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