# Find the inverse Laplace transform of (1)/((s^2+1)^2)

propappeale00 2022-10-12 Answered
Find the inverse Laplace transform of $\frac{1}{{\left({s}^{2}+1\right)}^{2}}$
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## Answers (1)

occuffick24
Answered 2022-10-13 Author has 13 answers
Hint:
${\mathcal{L}}^{-1}\left[\frac{1}{\left({s}^{2}+{\omega }^{2}{\right)}^{2}}\right]=\frac{1}{2{\omega }^{3}}\left(\mathrm{sin}\omega t-\omega t\mathrm{cos}\omega t\right)$
Note: $\omega$ is a real constant in this generalization.
Now, can you find the Laplace transform of $\mathrm{sin}\omega t$ and $\omega t\mathrm{cos}\omega t$ to understand what is going on with one of the shift theorems and why this is the result?
Of course you can always use the formal definitions to find this also if that is the approach required.
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