**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