Any suggestions for finding the inverse Laplace transform of 11/(s^2+16)^2?

[bmed90]

Hi,

I would like to find the inverse Laplace transform for

11/(s^2+16)^2

I have tried to expand it using the following partial fraction decomp to find the constants and take the inverse Laplace but this did not work

C1(s)+ C2/(s^2+16) + C3(s)+C4/(s^2+16)^2

Does anyone have any suggestions?

 

[lurflurf]

First try to find
$$\mathcal{L}^{-1} \left\{ \frac{1}{(s^2+16)} \right\}$$
Then use the integration rule
$$\mathcal{L}^{-1} \{ \mathrm{F}(s) \} = t \, \mathcal{L}^{-1} \left\{ \int_s^\infty \! \mathrm{F}(u) \, \mathrm{d}u \right\}
\\
\text{or the convolution rule}
\\
\mathcal{L}^{-1} \left\{ G(s)H(s) \right\} = \int_0^t g(t-\tau)h(\tau) \mathop{d\tau}
\\
\text{where}
\\
\mathcal{L}^{-1} \{ \mathrm{G}(s) \} =g(t)
\\
\mathcal{L}^{-1} \{ \mathrm{H}(s) \} =h(t)

$$