b) Find the function $f(t)$ whose Laplace transform is \(i) \ F(s) = \frac{4s^3 - 1}{s^4} \(ii) \ F(s) = \frac{3}{s^2 + 3s} [5 marks]
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In this case, we are given that: F(s) = 4 / (s - 0) = 4 / s So we can start by using the inverse Laplace transform to find f(t): f(t) = L^-1{F(s)} = L^-1{4 / s} To do this, we need to know the Laplace transform of 1/s, which is: L{1/s} = ∫[0,∞) e^(-st) (1/s) Show more…
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