MA231 Mathematics III Nov Dec 2007
MA231 Mathematics III Nov Dec 2007
MA231 Mathematics III Nov Dec 2007
Q 2381
B.E./B.Tech. DEGREE EXAMINATION. NOVEMBER/DECEMBER 2007. Third Semester Civil Engineering MA 231 - MATHEMATICS - III (Common to All Branches except Bio-Medical Engineering/Civil Engineering and Computer Based Construction/FashionTechnolory/Industrial Biotechnology/ Textile Chemistrv) ' Time : Three hours
^t
2.
3.
If cos3 =+*i{o,cosnt t
n=l 2.* A0 s-/ q ,o\
;*
4. 5. 6.
1\";+b;).
I
The Fourier seriesof x2 in (0,2) and that of (r + 2)2 in (-2,0) are identical or not. Give reasons. State any two assumptions involved in deriving one dimensional wave equation. How many conditions are required to solve Ou , d2u
E=o- a*,
7. Give an example of a function which has Laplace transform but it is not continuous. It LLfLJl= ---l(s - 2)'
ww
8.
w.
aa na
1.
va
N.
co m
9. 10.
Find the fourier sine transform of e-"" , a > 0 . State the shifting properties on fourier transform' PARTB-(5x16=80marks)
11. (a)
(i)
Form the p.d.e of the family of planes that are at constant distance k from the origin. SolveP' + q' = "'6' + Y')' Or
(ii)
(b)
(i) (ii;
S o l v e( y + r ) p + ( z + x ) q = x + Y . Solve (n' * DD' - 6D'2)z=! cosx. Find the fourier seriesexpansionof f (x) = x2 in (0,21)'
12. (a)
(i) (ii)
N.
co m
Find the half range sine seriesexpansionof f(x)=;-x and deducethe sum of the series i+ f;n"
tn (0,tt)
(ii)
w.
Find upto the first two harmonics in the fourier series of y f (x) tn (0, 360) gr.ven the following tabular value in x, 0o 60" L20" 180" 240" 300" 360' 2 2.1 3 3.2 2.5 2.2 2
(b)
(i)
ww
y
aa na
Or Or 2
va
13.
(a)
(i) (ii)
g+ t
Find the Laplace transform of the periodic function o''.to^ r @' = { t : - t . l2a . a <t <2a a n df ( t + 2 a ) = f ( t )
Q 2381
(b)
(i)
(ii)
14.
(a)
A string of length 21, fastened at both ends. Motion is started by dispiacing the string into the form y =kx(21-r) and then releasing it from this position at time t = 0 . Find the dispiacement of the point of the string at a distance* from one end at time '/'. Or
(b)
15.
(a)
(i)
(ii)
w.
M
*2
f (*) =
(b)
(i)
ww
Find the Fourier sine transform of f (*) = e-o* and hence evaluate
-r
@t
x'd x
c\2
I t
o\a'+x"1
(ii)
aa na
Or
provet'atTu?dx andhence
va
N.
Q 2381
co m
A rectangular plate of sides a and b has its faces insulated and the edges x J=0 and J=b andr=0 arekeptatOoCandtheedge =aiskeptat - b) . Find the steady state temperature distribution in temperature k(2y the plate.