Anna University Coimbatore 2009 B.E Electrical and Electronics Engineering Engineering Mathematics 3 - Question Paper
Wednesday, 16 January 2013 12:30Web
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Q.CODE: 081001
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Find the solution of yfp + /q = 1
Find the particular integral of [D2-3DD' + 2D'2]z = sin(x-2y)
Find the root mean square value of f(x)=x2 in the interval (0,271)
State Parsevals theorem on Fourier coefficients.
Prove that F[eiaxf(x)] = F(s + a) where F[ f(x) ]=F(s)
Find f(x), if fs(n) = -3, n = 1,2,3,.......oo and 0<x<7t
"I Q2\i
In the equation of motion of vibration of string , what does c2
B.E. / B.TECH. DEGREE EXAMINATIONS : NOV / DEC 2009
CIVIL / MECH / EEE / ECE / PRODN / EIE / CSE / IT / IBT BRANCHES 08C3Z1 /08M3Z1 /08E3Z1 /08L3Z1 /08P3Z1 /08N3Z1 /08S3Z1 /08I3Z1 /08B3Z1
ENGINEERING MATHEMATICS III (Common to PTBE)
du
dt 3x
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V -V.T
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Find z[eat+b]
Prove initial value theorem on z-transform.
PART -B
(5 x 16 = 80)
11. (a) Form the partial differential equation by eliminating f from the relation (8)
f (xy-z2, x2-y-z)=0
(b) Solve [D2 -DD' -2D'2]z = 2x + 3y + e3x+4y (8)
(OR)
12. (a) Solve x(z2-y2) p + y(x2-z2)q = z(y2-x2) (8) (b) Solve [D2 + 3DD'-4D/2]z=cos(2x + y) + xy (8)
13. (a)
2 Q.CODE: 081001
(8)
0 , 71 < x < 0
7tX n
-. 0 < X < 71
1 4
Find the Fourier expansion of f(x) =
Find the half range cosine series of x - x + in (0,1)
(OR)
14. (a) If f(x) = x - x2 in the range (0, {), find the half - range sine series of f(x). (8)
1111 Deduce that -T-r + -T- + 13 3 5 7
(b) Find the Fourier series y = f(x) upto second harmonics from the following data.
15 (a)
' Find the Fourier transform of e
(b) x2 *
Using transform method, find =- dx , a > 0
0J (x +az)
Find the Fourier transform of f(x) =
(b) x2
Find finite Fourier sine and cosine transform of x + in 0<x< n
3 27i
A string is stretched between two fixed points x=0 and x= I and released at (16)
rest from the initial deflection given by f(x) =
Find the deflection of the string at any time.
17.
-3- Q.CODE: 081001
(OR)
18. The ends A and B of a rod of length f cm are kept at 0C and 100C (16) respectively until steady state conditions prevail. The temperature at A is then suddenly raised to 50c and at the same time that at B to 150c, find the temperature distribution u(x,t) in the rod.
n(n + 1)
(b) Solve yn+2 + 2yn+i + yn = n given y0 = 0 and yi=0 using z-transform.
(OR)
Using convolution theorem, evaluate z
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