
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
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Chapter 15 Solutions
Fundamentals of Electric Circuits
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