(b) Using Convolution theorem evaluate $L^{-1}\left[\frac{s^{2}}{\left(s^{2}+4\right)^{2}}\right]$.

Explanation

The Convolution theorem is used to evaluate the inverse Laplace transform of $\frac{s^{2}}{\left(s^{2}+4\right)^{2}}$. The inverse Laplace transform of $F(s)G(s)$ is given by $f(t)g(t)=L^{-1}\left[\frac{1}{\left(s^{2}+4\right)^{2}}\right]$. The inverse Laplace transform of $F(s)$ is given by $f(t)=L^{-1}\left[\frac{s^{2}}{\left(s^{2}+4\right)^{2}}\right]=\frac{t}{4} \sin 2 t$.

(b) Using Convolution theorem evaluate $L^{-1}\left[\frac{s^{2}}{\left(s^{2}+4\right)^{2}}\right]$.

Explanation

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