Programmed tutorial: Inverse Laplace Transform Example 3a

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Find the inverse Laplace transform of
Inverse Laplace transform problem with a factored cubic 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

Add equations 1 and 2 to eliminate C.

We get

Equation 4

Add 6 times the equation 1 to the equation 3 to get another equation involving A and B.

We get

Equation 5

Now combine two times equation 4 and equation 5.

We get

Subtracting, we get

, or B = 1

Use this in equation 4 to find A.

, or A = 5

Use these results for A and B in equation 1 to find C.

, or C = –6

Use these results to rewrite F(s).

Which entry in the Table of Laplace Transforms matches the denominators?

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

a = 3, a = – 2, and a = – 4, respectively.

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