MEC702_Lab_Test - MEC702 Lab Test Weight 10 Marks total 30...

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Unformatted text preview: MEC702 Lab Test Weight: 10% Marks: total 30 marks (2 marks each question) Duration: 60 mins Software: MATLAB Instructions: You are required to write down the the 1. Solve the following second-order IVPs. (a) y 00 + 25y = 0, y(0) = 4.6, y 0 (0) = −1.2. (b) y 00 + y 0 − 6y = 0, y(0) = 10, y 0 (0) = 0. (c) x2 y 00 − 4xy 0 + 6y = 0, y(1) = 0.4, y 0 (1) = 0. Solution: (a) (b) (c) 2. Find the rst derivative of the following functions. (a) y = x2 cos x. (b) y = 3x+2 x2 +1 . Solution: (a) (b) 3. Integrate the following functions. (a) ´ e−t sin 2tdt. ´ √ (b) t t2 + 1dt. Solution: (a) (b) 1 output solution given by the program. 4. Find the eigenvalues and eigenvectors of the follow matrices.   2 1 (a) A = . 5 −2   0 1 (b) A = . −9 0 Solution: (a) (b) 5. Find the Laplace transform of the following functions. 1 sin 10t. (a) f (t) = 10 2 2t (b) f (t) = t e . Solution: (a) (b) 6. Evaluate the inverse Laplace transform. (a) (b) 1 s(s2 +36) . 1 (s−2)(s−3) . Solution: (a) (b) 7. Plot the following functions over the indicated interval. (a) y = sin 2x over [0, 4π]. (b) y = −e−x over [−3, 3]. Graphs: 2 ...
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  • Winter '16
  • Alveen Chand
  • Laplace, 10%, Eigenvalue, eigenvector and eigenspace, following functions, 60 mins

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