Find the Laplace transforms of the following functions, using the information in Table 3.1. (However, someof the individual terms in these functions may not have Laplace transforms.)
a.
b.
c.
d.
(a)
Interpretation:
Laplace transform of
Concept introduction:
For a function
Here,
Answer to Problem 3.1E
Explanation of Solution
The Laplace transform of the function of type
Laplace transform of the function of type
Laplace transform of the function of type
Now, for the given function
For
For
For
Combine the Laplace transformsof
(b)
Interpretation:
Laplace transform of
Concept introduction:
For a function
Here,
Answer to Problem 3.1E
Explanation of Solution
The Laplace transform of the function of type
Laplace transform of the function of type
The Laplace transform of the function of type
The Laplace transform of the function of type
Now, for the given function
For
For
For
For
For
Combine the Laplace transforms of
(c)
Interpretation:
Laplace transform of
Concept introduction:
For a function
Here,
Answer to Problem 3.1E
Explanation of Solution
The Laplace transform of the function of type
The Laplace transform of the function of type
Now, for the given function
For
For
Combine the Laplace transforms of
(d)
Interpretation:
Laplace transform of
Concept introduction:
For a function
Here,
Answer to Problem 3.1E
Explanation of Solution
Simplify the given function and expand using the formula
Note that
The Laplace transform of the function of type
The Laplace transform of the function of type
The Laplace transform of the function of type
The Laplace transform of the function of type
The Laplace transform of the function of type
Now, for the simplified function
For
For
For
For
For
Combine the Laplace transforms of
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