How To Exam?

# Anna University Coimbatore 2009 B.E Transforms and Partial Differential Equation - Model - Question Paper

Wednesday, 16 January 2013 07:10Web

MODEL EXAMINATION

MODEL EXAMINATION

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATION

Year/Semester & Branch: II / III Common to all Branches

Max. Marks: 100 Time: 180 min

1.      Determine the value of in the Fourier series expansion of  . (A/M 08)

2.      Define Root mean square of over the range . (Tri-N/D 08)

3.      If in the interval (0,4), then find the value of in the Fourier series expansion. (Cbe-N/D 08)

1. State Dirichlets condition for Fourier series. (Tnl-N/D 08) (Nov 05)
2. Let be the Fourier cosine transform of . Prove that . (Cbe-N/D 08)
3. State Fourier integral theorem. (A/M 08) (Cbe-N/D 08)
4. If then prove that (Tnl-N/D 08)
5. what is the sine transform of if is the Fourier sine transform of .(Tri-N/D 08)
6. Form the partial differential equation by eliminating arbitrary constants from (Cbe-N/D 08)
7. Find the complete integral of (N/D 08).
8. Eliminate the function f from (Tnl-N/D 08).
9. Write the complete integral of (Tnl-N/D 08)
10. A rod 50cm long with insulated sides has its ends A and B kept at and respectively. Find the steady state temperature distribution of the rod. (Cbe-N/D 08)
11. Classify the partial differential equation . (A/M 08)
12. Write the initial conditions of the wave equation if the string has an initial displacement but no initial velocity. (Tnl-N/D 08)
13. List all the possible solutions of the one dimensional wave equation and state the proper solution. (Tri-N/D 08)
14. Form the difference equation from . (A/M 08)
15. Find (A/M 08) (Tnl-N/D 08)
16. If What is ? (Tri-N/D 08)
17. Find the Z- transform of . (Tri-N/D 08)

PART-B (Answer ANY 5 questions) (5 X 12 = 60)

1. a) Obtain the Fourier series of of period 2l and defined as follows .Hence deduce (Tnl-N/D 08)

b) Find the half range sine series of in (Tnl-N/D 08)

1. Find the Fourier cosine transform of  . Hence prove that (Tnl-N/D 08)
2. a) Solve .(Tri-N/D 08)

b) Solve .(Tri-N/D 08)

1. If a string of length l is initially at rest in its equilibrium position and each of its points is given a velocity v such that   . Determine the displacement function at any time t.(Cbe N/D 08)
2. a) Find the Z-transform of and . Hence find .

b) Solve using Z-transform given .

1. a) Obtain the Fourier series upto second harmonic from the data

x : 0       : 0.8 0.6 0.4 0.7 0.9 1.1 0.8 (Cbe N/D 08)

b) Find the Fourier cosine transform of . Hence deduce the value of .(Tri-N/D 08)

1. The ends A and B of a rod l cm long have their temperatures kept at and , until steady state conditions prevail. The temperature at the end B is suddenly reduced to and that of A is increased to .Find temperature distribution in the rod after timet.(Tnl-N/D 08)

1. a) Find using Convolution theorem. (Tnl-N/D 08)

b) Find the singular integral of . (Cbe N/D 08) 