Laplace Transforms: Convolution Theorem

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Eli
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#1

Convolution Theorem is very powerful for finding inverse Laplace Transforms. This theorem states that: If and are piecewise continuous on and of exponential order, then

.

Let's apply Convolution Theorem to find

.

Let ,

so that ,

.

Thus

Recall from trigonometry:

, and

,

so

If we set ;



=

=
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