Programmed tutorial: Inverse Laplace Transform Example 2a

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Find the inverse Laplace transform of

How do we go about finding entries in the Table of Laplace Transforms?

For each term, we compare its denominator with those in the table.

Which entry in the table matches the denominator?

#7 and #8 have the s² and the additive constant.

What disagrees?

We need to do something like take a square root of the 3.

Rewrite accordingly.

What is the value of “a” here?

Does the numerator match #7 or #8?

No.

How can we fix it?

It will come closer to matching if we write it as the sum of two fractions.

Do that.

Adjust the constants in the numerator.

We get

Do the numerators now match #8 and #7?

Almost. We need

in the second term.

How can we obtain this?

We can multiply by

Rewrite accordingly.

It becomes

Find the inverse Laplace transform.

We get
ℒ Inverse Laplace Transform, sum of squares in denominator

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