Programmed tutorial: Laplace Transform Example 2

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Find the Laplace transform of

using the Table of Laplace Transforms.а

First decide what effect the factors У3Ф, УЦ2Ф, and У6Ф have.

These multipliers are simply applied to the transform in the table.

Which transform from the Table can be used on the first term,

Transform #7.

What is the value of УaФ here?

a = 5.

State the result for this term.

ℒ

In the second term,

we have a cosine and a negative coefficient.а Do we need to find another entry in the table?а If so, which one?

Yes, #8.

How can we use #8 here where we have a negative coefficient?

We can take a а= аЦ 5.

What about the 2?

It appears in the result as a multiplier.

State the result of the substitution for this term.

ℒ

Simplify the denominator.

ℒ

In the third term, we have a cosine of a fractional coefficient to transform: ℒ

Which transform from the table should we use?

We can use #8 again.

What is the value of a?

State the result for this term.

ℒ

Simplify the denominator.

ℒ $Laplace transform of the cosine with fractional coefficient$

Have we finished the problem?

No.

What more do we need to do?

We need to combine the results obtained for the separate terms.

Do that.

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