Sathyabama University 2007 B.E Mechanical Engineering Mathematics - II -6CPT0009 - Question Paper

SATHYABAMA UNIVERSITY
(Established under part three 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: three Hours
Date: 16-05-2008 Session: FN

PART – A (10 x two = 20)
ans All the ques.
1. Write the Dirichlet’s conditions?
2. State the Euler’s formula for the interval (c, c + 2l).
3. Form the partial differential formula by eliminating the arbitrary constants a and b from Z = (x2 + a) (y2 + b).
4. obtain the completer integral of P2 + q2 = 1.
5. Write down the 3 possible solns of wave formula.
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 every end in suddenly decreased to zero degree centigrade and dept so. Write the boundary conditions.
7. Write down the 3 possible solns of 2 dimensional heat formula 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. obtain the fourier cosine trans form of





PART – B (5 x 12 = 60)
ans All the ques.

11. (a) obtain 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) obtain the foureir series of f(x) of Period four provided by

(b) obtain the complex form of the fourier series of f(x) = ex in -? < x < ?.

13. (a) Solve p2(1 + x2)y = qx2.

(b) obtain 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 identical instant that at B is lowered to 60?C and temperature are maintained there after. obtain 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 every point a velocity ?x(l – x), obtain the displacement.

17. The temperature u is maintained at 0?C along 3 edges of a square plate of length 100?C cm and the 4th edge is maintained at a constant temperature u0 until steady-state conditions prevail. obtain an expression for the temperature u at any point (x, y) of the plate. compute 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. obtain the fourier transform of f(x) provided by

and hence evaluate (i)
(ii)
(or)
20. (a) obtain the foureir cosine transform of .
(b) Evaluate using transform methods.

Earning:   Approval pending.