Inverse Laplace Transform of $$$\frac{1}{s \left(\frac{s}{s + 1} + \frac{2}{2 s + 1}\right)}$$$
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Find $$$\mathcal{L}^{-1}_{s}\left(\frac{1}{s \left(\frac{s}{s + 1} + \frac{2}{2 s + 1}\right)}\right)$$$.
Answer
The Inverse Laplace transform of $$$\frac{1}{s \left(\frac{s}{s + 1} + \frac{2}{2 s + 1}\right)}$$$A is $$$\frac{1}{2} + \frac{3 \sqrt{7} e^{- \frac{3 t}{4}} \sin{\left(\frac{\sqrt{7} t}{4} \right)}}{14} + \frac{e^{- \frac{3 t}{4}} \cos{\left(\frac{\sqrt{7} t}{4} \right)}}{2}$$$A.
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