MEC702_Short_Test_3

# MEC702_Short_Test_3 - MEC702 Short Test 2 Mode Semester...

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Unformatted text preview: MEC702 Short Test 2 Mode: Semester Weight: 2, 2015 15% Total Marks: 30 Duration: mins 60 marks Exercise. 1. Solve the following initial value problem. y10 = y1 + y2 , y20 y1 (0) = 1, y2 (0) = 6 = 4y1 + y2 (6 marks) 2. Determine the type of critical point and its stability as well. y10 = 2y1 + y2 y20 = 5y1 − 2y2 (6 marks) 3. Solve the IVPs by the Laplace transform. Show all details. a.) y 0 + 5.2y = 19.4 sin 2t, b.) 00 0 y − y − 6y = 0, y(0) = 0 y(0) = 11, y 0 (0) = 28 (6 + 6 marks) 4. Determine if the given function is odd or even or neither. Find the Fourier series for the function. Show details of your work. ( f (x) = 0, −π < x < 0 , 1, 0 < x < π period p = 2L. (6 marks) 1 ...
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