QUESTION 3 (15 MARKS) (a) Find the Laplace transform of the following periodic function. (b) Find f(t), if given f(t)= 0

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Question 3 15 Marks A Find The Laplace Transform Of The Following Periodic Function B Find F T If Given F T 0 1 (21.02 KiB) Viewed 22 times

QUESTION 3 (15 MARKS) (a) Find the Laplace transform of the following periodic function. (b) Find f(t), if given f(t)= 0, f(t) = f(t + 2x). f(1) = C-1 Hence show that f(3) = e-³. given that r(0)= 0 and (c) Solve the following boundary value problem z" +9z6(t-3m), () = -3. QUESTION 4 (15 MARKS) (a) Use the convolution theorem to find Ost≤T * < x < 2n 2e-2 (8+3)³ C²₁ { (~² + 1)²} - (b) Solve the following system of differential equations x-2y 2x + y = 20 (4 marks) (6 marks) (5 marks) (7 marks) using the method of Laplace transform. Given that z(0)= y(0) = 0. (8 marks)