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

Wednesday, 30 January 2013 12:40Web

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 Ma

**x.**

**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 circumferenc

**e.**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.

**1**

**1.****(**obtain the fourier series of f

**a)****(**= x + x2 in (-?, ?) of periodicity 2?. Hence deduce

**x)****(**Expand f

**b)****(**= x sinx as a cosine series in 0 < x < ? and show that

**x)**(or)

**1**

**2.****(**obtain the foureir series of f

**a)****(**of Period four provided by

**x)****(**obtain the complex form of the fourier series of f

**b)****(**= ex in -? < x < ?.

**x)****1**

**3.****(**Solve p2(1 + x2)y = qx2.

**a)****(**obtain the general soln of x(z2 – y

**b)****2)**p + y(x2 – z2)q = z(y2 – x2)

(or)

**1**

**4.****(**Solve (D3 – 2D2D1)z = Sin (x + 2y) + 3x2y.

**a)****(**Form the PDE by eliminating f from z = xy + f(x2 + y2 + z2).

**b)****1**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.

**5.**(or)

**1**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.

**6.****1**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 plat

**7.****e.**compute the temperature at the centre of the plate.

(or)

**1**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)?.

**8.****1**obtain the fourier transform of f

**9.****(**provided by

**x)**and hence evaluate (i)

(ii)

(or)

**20.**

**(**obtain the foureir cosine transform of .

**a)****(**Evaluate using transform methods.

**b)**Earning: Approval pending. |