2. Find the inverse Laplace transform of each of the following: a) (s - 2)^4 b) (s - 3)/(s - 2)^2 + 16 c) (e^(-2t))/(s^2 + 1) d) 5/(2 + 3s)
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To find the inverse Laplace transform of $(s-2)^4$, we can use the formula for the inverse Laplace transform of $s^n$: $$\mathcal{L}^{-1}\{s^n\} = \frac{t^{n-1}}{(n-1)!}u(t)$$ So, for $(s-2)^4$: $$\mathcal{L}^{-1}\{(s-2)^4\} = \frac{(t-2)^{4-1}}{(4-1)!}u(t-2) = Show more…
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