KARAIKUDI INSTITUTE OF TECHNOLOGY KARAIKUDI INSTITUTE OF TECHNOLOGY KIT & KIM TECHNICAL CAMPUS KIT & KIM TECHNICAL CAMPUS Keeranipatti, Thalakkavur, Karaikudi – 630 307 Keeranipatti, Thalakkavur, Karaikudi – 630 307
UNIT TEST-III MAR 2014(I YEAR B)(Answer All the
Questions)PART A -
2 Mark Qs (5x2=10)1.State Gauss divergence theorem. 2.Define periodic function..3.Write down any two properties of Laplace transform .4.State sufficient conditions for existence of Laplace transform. .5.Give two examples for a function for which Laplace transform does not exist.
PART B – (1x8=8 Mark)(2x16=32 Mark)6 Find the Laplace transform for the following functions. (a).sin2 3 t (b).sin 2 tcost (c).cos2 tcos 5t (d).(a+bt )2
7.(i).Verify Stokes theorem for For F⃗=− y i⃗+2 yz j⃗+ y2 k⃗ where S is the upper half
of the sphere x2+ y2+z2=a2 and C is the boundary on the xoy plane. (OR)
(ii)Verify divergence theorem for F⃗=x2 i⃗+z j⃗+ yz k⃗ over the cube formed by
x=±1 , y=±1 , z=±1. 9.(i).Find the Laplace transform for the following functions.
(a).eat−cosbtt
(b).∫0
∞
t e−2 t cos2t
(ii).Find (a) L(tsin3 t) (b)L(e−5 t cos 4 t) (c) L(t e−4 t sin 3 t)
10.(i). Find the Laplace transform of f ( t )=kt ,0<t<1 , suchthatf ( t+1 )=f (t )
(ii). Find the Laplace transform of f (t )={ t∈0<t<a2a−t∈a<t<2a .
and
f ( t+2a )= f (t ) (OR)
11.(i). Find the Laplace transform of f ( t )={asinωt∈0<t< πω
0∈ πω
< t< 2πω.
and
f (t+ 2 πω )=f (t)
(ii). Find the Laplace transform of f (t )=et ,0< t<2π , suchthatf ( t+2π )=f (t ) .
UNIT TEST-III(I YEAR B)
(Answer All the Questions)PART A - 2 Mark Qs (5x2=10)
1.State Gauss divergence theorem. 2.Define periodic function..3.Write down any two properties of Laplace transform .4.State sufficient conditions for existence of Laplace transform. .5.Give two examples for a function for which Laplace transform does not exist.
PART B – (1x8=8 Mark)(2x16=32 Mark)6 Find the Laplace transform for the following functions. (a).sin2 3 t (b).sin 2 tcost (c).cos2 tcos 5t (d).(a+bt )2
7.(i).Verify Stokes theorem for For F⃗=− y i⃗+2 yz j⃗+ y2 k⃗ where S is the upper half
of the sphere x2+ y2+z2=a2 and C is the boundary on the xoy plane. (OR)
(ii)Verify divergence theorem for F⃗=x2 i⃗+z j⃗+ yz k⃗ over the cube formed by
x=±1 , y=±1 , z=±1. 9.(i).Find the Laplace transform for the following functions.
(a).eat−cosbtt
(b).∫0
∞
t e−2 t cos2t
ENGINEERING MATHEMATICS-II 50 Marks
ENGINEERING MATHEMATICS-II 50 Marks
KARAIKUDI INSTITUTE OF TECHNOLOGY KARAIKUDI INSTITUTE OF TECHNOLOGY KIT & KIM TECHNICAL CAMPUS KIT & KIM TECHNICAL CAMPUS Keeranipatti, Thalakkavur, Karaikudi – 630 307 Keeranipatti, Thalakkavur, Karaikudi – 630 307
(ii).Find (a) L(tsin3 t) (b)L(e−5 t cos 4 t) (c) L(t e−4 t sin 3 t)
10.(i). Find the Laplace transform of f ( t )=kt ,0<t<1 , suchthatf ( t+1 )=f (t )
(ii). Find the Laplace transform of f (t )={ t∈0<t<a2a−t∈a<t<2a .
and
f ( t+2a )= f (t ) (OR)
11.(i). Find the Laplace transform of f (t )={asinωt∈0<t< πω
0∈ πω
< t< 2πω.
and
f (t+ 2 πω )=f (t)
(ii). Find the Laplace transform of f (t )=et ,0< t<2π , suchthatf ( t+2π )=f (t ) .
PART A - 2 Mark Qs (5x2=10)
1.State Newton’s formula to find f '( x) using forward differences. 2.What is the restriction on number of intervals in Simpson’s 3/8 rule. .3.State two point Gaussian quadrature formula .
4.Solve dydx
=1− y , y (o )=0 for x=0.1 by Euler’s method.
5.State Trapezoidal rule to evaluate ∫x0
xn
f ( x )dx .
PART B – (1x8=8 Mark)(2x16=32 Mark)
6.Compute the value of ∫4
5.2
logx dx by dividing the range into 6 equal parts by using
Trapezoidal rule.
7.(i).For the given data, find dydx
and d2 yd x2 at x=1.1.
x 1 1.1 1.2 1.3 1.4 1.5 1.6 f(x) 7.989 8.403 8.781 9.129 9.451 9.750 10.031
(ii)Evaluate ∫0
2 dxx2+4
using Romberg’s method.
8.(i).When a train is moving at 30 meters per second steam is shut off and breaks are applied. the speed of the train (V) in meters per second after t seconds is given by
t 0 5 10 15 20 25 30 35 40 v 30 24 19.5 165 13.6 11.7 10 8.5 7
(ii). Evaluate ∫0
1
∫1
2 2 xydxdy(1+x2 )(1+ y2)
by Trapezoidal rule with h=k=0.
9.(i).Using Simpson’s rule ,evaluate
∫4
4.4
∫2
2.6 dxdyxy
h=0.3 and k=0.2.
(ii).Using Runge- Kutta method of fourth order solve
y '= y2−x2
y2+x2 with y (0 )=1at x=0.2,0 .4 .
10.(i).Using improved Euler’s method find y(0.2) and y(0.4) from y '=x+ y , y (0 )=1with h=0.2. (ii). Consider the second order initial value problem
d2 yd x2 −2 dy
dx+2 y=e2x sinx with y (0 )=−0.4∧ y ' (0 )=−0.6, using Fourth
order RK method find y(0.2). (Answer All the Questions)PART A - 2 Mark Qs (5x2=10)1.Locate the negative root ofx3−2 x+5=02. What is the condition for convergence of Gauss-Jacobi method.3. Give Lagrange’s inverse interpolation formula.4. Write divided difference table for x 30 35 45 55y 148 96 68 34
KARAIKUDI INSTITUTE OF TECHNOLOGY KARAIKUDI INSTITUTE OF TECHNOLOGY KIT & KIM TECHNICAL CAMPUS KIT & KIM TECHNICAL CAMPUS Keeranipatti, Thalakkavur, Karaikudi – 630 307 Keeranipatti, Thalakkavur, Karaikudi – 630 307
5. Give Newton’s forward interpolation formula.
PART B – (1x8=8 Mark)(2x16=32 Mark)6. Solve x+ y+54 z=110 ;27 x+6 y−z=85 ;6 x+15 y+2 z=72 ,by Gauss Seidel method.
(i) Use Power method to find the dominant eigen value and eigen vector of [ 2 −1 0−1 2 −10 −1 2 ]
(ii) Solve10 x−2 y+3 z=23 ;2x+10 y−5 z=−33 ;3 x−4 y+10 z=41by Gauss elimination method.(i). Find the equation of the parabola passing through the points (0,0),(1,1)and (2,20) using Lagrange’s formula. (ii). Use Newton’s divided differences formula to find f(3)from the data
x 0 1 2 4 5 f(x) 1 14 15 5 6
Find the cubic spline approxi,ation and hence find f(1.5)x 1 2 3 4 f(x) 1 2 5 11
11.(i)Find the values of y at x=21 and x=28 from the data given below
(ii)Solve sinx=1+x3lies between (-2,-1) to 3 decimal places by Newton Raphson method.
INTERNAL TEST-I FEB 2014ME2026 – UNCONVENTIONAL MACHINING PROCESS 50
Time: 09:15 a.m. – 11:00 a.m. Marks
(Answer All the Questions)PART A - 2 Mark Qs (5x2=10)
1.What are the industrial needs for UCM?2.List down the various mechanical energy based Unconventional Machining Processes.3.What are the different machining characteristics will respect to which the non-traditional machining processes can be analyzed?4.Distinguish traditional & non-traditional machining processes?5.How will you compare various non-traditional processes?
PART B – 1x8=8 Mark2x16=32 Mark
6. What is the need for the development of UCM process? Explain with examples. (8)7. Make a comparison between traditional and unconventional machining processes in terms of cost, application, scope, machining time, advantages & limitations. (16)
(OR)8.With a neat sketch explain the process of AJM? Write its advantages and applications.(16)
9. Make a comparison between traditional and unconventional machining processes in terms of cost, application, scope, machining time, advantages & limitations.(16)
(OR)10.Discuss the effects of the following parameters on the material removal and surface finish in ultrasonic machining:
a. Amplitude and frequencyb. Abrasive sizec. Concentration of abrasivesd. Material hardness
x 20 23 26 29y 0.3420 0.3907 0.4384 0.4848
KARAIKUDI INSTITUTE OF TECHNOLOGY KARAIKUDI INSTITUTE OF TECHNOLOGY KIT & KIM TECHNICAL CAMPUS KIT & KIM TECHNICAL CAMPUS Keeranipatti, Thalakkavur, Karaikudi – 630 307 Keeranipatti, Thalakkavur, Karaikudi – 630 307
INTERNAL TEST-I FEB 2014ME2026 – UNCONVENTIONAL MACHINING PROCESS
Time: 09:15 a.m. – 11:00 a.m.50
Marks
(Answer All the Questions)PART A - 2 Mark Qs (5x2=10)
1.What are the industrial needs for UCM?2.List down the various mechanical energy based Unconventional Machining Processes.3.What are the different machining characteristics will respect to which the non-traditional machining processes can be analyzed?4.Distinguish traditional & non-traditional machining processes?5.How will you compare various non-traditional processes?
PART B – 1x8=8 Mark2x16=32 Mark
6. What is the need for the development of UCM process? Explain with examples. (8)7. Make a comparison between traditional and unconventional machining processes in terms of cost, application, scope, machining time, advantages & limitations. (16)
(OR)8.With a neat sketch explain the process of AJM? Write its advantages and applications.(16)
9. Make a comparison between traditional and unconventional machining processes in terms of cost, application, scope, machining time, advantages & limitations.(16)
(OR)10.Discuss the effects of the following parameters on the material removal and surface finish in ultrasonic machining:a. Amplitude and frequencyb. Abrasive sizec. Concentration of abrasives
d. Material hardness