Find the Laplace transform of each of the following five functions. (1) f(t) = t^3 + 2t^2 - 3t + 5 (2) f(t) = sin(3t) + e^3t (3) f(t) = t^2 e^4t (4) f(t) = cosh(t + 5) U(t + 5) (5) f(t) = t sin(t)
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L{t^3} = 3! / s^4 = 6 / s^4 L{2t^2} = 2 * (2! / s^3) = 4 / s^3 L{-3t} = -3 / s^2 L{5} = 5 / s So, the Laplace transform of f(t) is: F(s) = 6 / s^4 + 4 / s^3 - 3 / s^2 + 5 / s (2) f(t) = sin(3t) + e^t Again, using the linearity property, we can find the Show more…
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