Programmed tutorial: Inverse Laplace Transform Example 3b

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Find the inverse Laplace transform of
Inverse Laplace transform problem with a linear and a difference of squares in the denominator

How can we proceed?

We can rewrite F(s) in terms of partial fractions.

Set that up.

Combine the fractions.

Do the multiplication.

Collect like terms.

Equate the coefficients of like powers.

Using the numerators of the last equation, we get

Equation 1

Equation 2

Equation 3

Solve the first equation for B.

We get B = –A

Use this to rewrite equation 2 in terms of A and C.

We get 3A + C = 10 Equation 4

Now combine (three times equation 4) and equation 3.

We get

Adding, we get

, or A = 2

Use this in equation 3 to find C.

, or C = 4

Use the result for A in equation 1 to find B.

B = -2

Use these results to rewrite F(s).

Which entries in the Table of Laplace Transforms match the denominators?

For the first term, #2.
For the second term, #7, #8.

What are the values of “a” in each fraction?

a = 3 and

Determine the inverse Laplace transform.

ℒ

The end. If you found this helpful and would recommend that I create more pages like this one, please let me know: Email to John Taylor