Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below. t e^{5t} cos 7t L{t e^{5t} cos 7t} =
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Substitute values for s in the Laplace transform equation. Show more…
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Sri K.
Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below. Note that an appropriate trigonometric identity may be necessary. sin 7t sin 3t L{sin 7t sin 3t} =
Adi S.
Find the Laplace Transform of the following functions: (a) f(t) = cos(t) if 0 < t < 2; f(t) = 0 if t > 2. Rewrite using the step function; then find the Laplace transform: f(t) = 1 if 0 < t < 1/2; f(t) = -1 if 1/2 < t < 1; f(t) = 0 if t > 1. Rewrite using step functions, then find the Laplace transform. (c) f(t) = t^2 + 4(t - 3)^2. Find the inverse Laplace Transform of the following functions: F(s) = 4s / (s^2 + 9). F(s) = 8s / (s^2 - 9). Use the Laplace Transform to solve the following initial value problems: 1" + 4y' = 2u_1(t) - u_a(t); y(0) = 1, y'(0) = 0. 2" + 2y' + y = t + 6e^(-t); y(0) = 0, y'(0) = 2. 2" + 4y' + 5y = 0(t - 2) + 8(t - 2); y(0) = 0, y'(0) = 2.
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