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Posted Date: 19 Jul 2009 Posted By: Nitesh Chitranshi Member Level: Silver
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2008 SATHYABAMA UNIVERSITY B.Tech B.E Mechanical Engineering Mathematics - II -6CPT0009 Question paper Question paper
B.E Mechanical Engineering Mathematics - II -6CPT0009 Question paper
SATHYABAMA UNIVERSITY
(Established under section 3 of UGC Act, 1956)
Course & Branch: B.E/ B. Tech – CSE/ECE/EEE/CIVIL/MECH/
CHEM (Part Time)
Title of the paper: Engineering Mathematics - II
Semester: II Max. Marks: 80
Sub.Code: 6CPT0009 (2006/2007/2007 JAN) Time: 3 Hours
Date: 16-05-2008 Session: FN
PART – A (10 x 2 = 20)
Answer All the Questions
1. Write the Dirichlet’s conditions?
2. State the Euler’s formula for the interval (c, c + 2l).
3. Form the partial differential equation by eliminating the arbitrary constants a and b from Z = (x2 + a) (y2 + b).
4. Find the completer integral of P2 + q2 = 1.
5. Write down the three possible solns of wave equation.
6. An insulated rod of length l has its ends A and B kept at a degree centigrade and b degree centigrade until steady state conditions prevail. The temperature at each end in suddenly reduced to zero degree centigrade and dept so. Write the boundary conditions.
7. Write down the three possible solns of two dimensional heat equation in polar co-ordinates.
8. A Semi circular at 0?C on the bounding diameter and 100?C on its circumference. Write the corresponding boundary condition.
9. Write change of scale property.
10. Find the fourier cosine trans form of
PART – B (5 x 12 = 60)
Answer All the Questions
11. (a) Find the fourier series of f(x) = x + x2 in (-?, ?) of periodicity 2?. Hence deduce
(b) Expand f(x) = x sinx as a cosine series in 0 < x < ? and show that
(or)
12. (a) Find the foureir series of f(x) of Period 4 given by
(b) Find the complex form of the fourier series of f(x) = ex in -? < x < ?.
13. (a) Solve p2(1 + x2)y = qx2.
(b) Find the general soln of x(z2 – y2) p + y(x2 – z2)q = z(y2 – x2)
(or)
14. (a) Solve (D3 – 2D2D1)z = Sin (x + 2y) + 3x2y.
(b) Form the PDE by eliminating f from z = xy + f(x2 + y2 + z2).
15. A bar of length 20cm has it’s a and at 30?C and 80?C until steady-state conditions Prevail, the temperature at A is rexised to 40?C and at the same instant that at B is lowered to 60?C and temperature are maintained there after. Find the temperature at distance X form the end A at time t.
(or)
16. A tightly stretched string with fixed ends pts x = 0 and x = l is initially at rest in its equilibrium position. If it is set vibrating giving each point a velocity ?x(l – x), find the displacement.
17. The temperature u is maintained at 0?C along three edges of a square plate of length 100?C cm and the fourth edge is maintained at a constant temperature u0 until steady-state conditions prevail. Find an expression for the temperature u at any point (x, y) of the plate. Calculate the temperature at the centre of the plate.
(or)
18. In a semicircular plate of radius a with bounding diameter at 0?C and the circumference at t?C, show that the steady-state temperature distribution is gun by sin (2n – 1)?.
19. Find the fourier transform of f(x) given by
and hence evaluate (i)
(ii)
(or)
20. (a) Find the foureir cosine transform of .
(b) Evaluate using transform methods.
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