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# Anna University Coimbatore 2008 B.E Transforms and Partial Differential Equation - Model - Question Paper

Wednesday, 16 January 2013 07:15Web

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. If Find constant term of its Fourier series.(Tri-N/D 08)
2. Find the root mean square value of in the interval . (A/M 08)
3. State Dirichlets condition for Fourier series. (Tnl-N/D 08) (Nov 05)
4. The Fourier series expansion of in is . Find the root mean square value of in the interval . (Cbe-N/D 08)
5. State the Convolution theorem of the Fourier transform. (A/M 08)
6. State Fourier integral theorem. (A/M 08) (Cbe-N/D 08)
7. Write the Fourier transform pair (N/D 07).
8. Find the Fourier sine transform of . (N/D 07).
9. Find the complete integral of (Cbe-N/D 08)
10. Form a partial differential equation by eliminating arbitrary constants a and b from . (A/M 08)
11. Solve (A/M 08).
12. write the complete integral of . . (Tnl-N/D 08)
13. Classify the differential equation (Cbe-N/D 08)
14. The ends A and B of a rod of length 10cm long have their temperature kept at and . Find the steady state temperature distribution of the rod. (A/M 08)
15. Find the steady state temperature distribution in a rod of length 10cm whose ends x=0 and x=10 are kept at and respectively. (Tri-N/D 08)
16. Write the initial conditions of the wave equation if the string has an initial displacement but no initial velocity. . (Tnl-N/D 08)
17. Form a difference equation by eliminating arbitrary constants from .(Cbe-N/D 08)
18. Define Z-transform of the sequence (Cbe-N/D 08)
19. If What is ? (Tri-N/D 08)
20. Prove that . (Apr/May 1999), (Apr/May 2000)

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

1. a) Obtain Fourier cosine series for in .(Tri-N/D 08)

b) Compute the first two harmonics of the Fourier series of given in

the following table:

x : 0       : 1.0 1.4 1.9 1.7 1.5 1.2 1.0 (A/M 08)

1. Find the Fourier transform of   . Hence show that and (Cbe- N/D 08)
2. a) Solve (Cbe- N/D 08)

b) Solve (Cbe- N/D 08)

1. A rectangular plate with insulated surface is 10 cm wide and so long compared to its width that it may be considered infinite in length without introducing appreciable error. The temperature at short edge y=0 is given by   and all the other three edges are kept at . Find the steady state temperature at any point in the plate. (A/M 08)
2. a) Find the Z-transform of and (Cbe- N/D 08)

b) Find the inverse Z-transform of (Cbe- N/D 08)

1. a) Find the Fourier sine series for in (Tri-N/D 08)

b) Find the Fourier transform of   (Tri-N/D 08)

1. A string is stretched and fastened to two points l apart. Motion is started by displacing the string into the form of the curve and then releasing it from this position at time t=0. Find the displacement of the point of the string at a distance x from one end at time t . (A.U.Tri. Nov/Dec 2008) (Dec 2008) (May/June 2009)
2. a) Solve given , using Z-transform (Tnl-N/D 08)

b) Solve (A/M 08) 