- #1

zachdr1

- 91

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## Homework Statement

[tex] F(s) = \frac{s^2e^{-4s}}{s^2+9}[/tex]

## Homework Equations

[tex] \mathcal{L} ({f(t-a)\mathcal{H}(t-a)}) = e^{-as}F(s) [/tex]

## The Attempt at a Solution

[tex] F(s) = e^{-4s}(\frac{s^2}{s^2+9}) [/tex]

using [tex] \mathcal{L} {f(t-a)\mathcal{H}(t-a)} = e^{-as}F(s) [/tex]

[tex] f(t) = cos(3t-12)\mathcal{H}(t-4) [/tex]

I do not understand why this is incorrect. My professor got [tex]f(t) = \delta(t - 4) - 3sin(3t - 12)\mathcal{H}(t-4) [/tex]

EDIT: Wow I get it now, it's because [tex] \mathcal{L}(cos(kt)) = \frac{s}{s^2+k} [/tex] not [tex]\mathcal{L}(cos(kt)) = \frac{s^2}{s^2+k} [/tex] stupid mistake lol

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