Question: fQ4. Using the Fourier transform pairs table listed in the lecture note, please determine the Fourier transform of: a. f (t) = e-(@2+2+2abt), (5 points)

$\fQ4. Using the Fourier transform pairs table listed in the lecture$ note, please determine the Fourier transform of: a. f (t) = e-(@2+2+2abt), (5 points) b. f(t) = sin 2at. (5 points) Q5. Using the

solution of the following ODE a. f' (t) = 3e-1/2to(t) (5 points)

\fQ4. Using the Fourier transform pairs table listed in the lecture note, please determine the Fourier transform of: a. f (t) = e-(@2+2+2abt), (5 points) b. f(t) = sin 2at. (5 points) Q5. Using the Fourier transform pairs table listed in the lecture note, please determine the solution of the following ODE a. f' (t) = 3e-1/2to(t) (5 points) b. 3f'(t) + 4f (t) = e-to(t) (5 points)f.(t) 2a t a 2(t + a), - astso f(t) = -2(t - a), Ostsa 0, otherwise Find the Fourier transform of f(t). (10 points)

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