Solve question 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Solve question 3.
1. An 11-m beam is subjected to a load, and the shear force follows the equation
V(x) = 5 + 0.25x²
where V is the shear force and x is length in distance along the beam. We know that V = dM/dx, and M
is the bending moment. Integration yields the relationship
M = M, +
Vdx
If Mo is zero and x 12, calculate M using
a) trapezoidal rule with 1 m stepsize
b) Simpson's 1/3 rule with 1 m stepsize
c) Simpson's 3/8 rule with I m stepsize.
2. Please use the following data to calculate f (7) via linear, quadratic, cubic and quartic
interpolation.
2.5
3.5
5
6
7.5
10
12.5
15
17.5
f(x)
13
11
8.5
8.2
7
6.2
5.2
4.8
4.8
3. Please use the following dața to calculate f (x = 4.5, y = 3.2) via bilinear interpolation.
x = 2
90.00
|x = 8
x = 0
100.00
x = 4
80.00
r= 6
y = 0
70.00
60.00
53.50
y = 2
y = 4
y = 6
85.00
64.49
48.15
50.00
70.00
55.00
48.90
38.78
38.43
30.39
35.03
27.07
25.00
40.00
30.00
20.00
y = 8
40.00
35.00
30.00
4. Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25
where y(0) = 1.
dy
= (1 + 2x)/y
dx
a) Euler's method
b) Heun's method without the corrector.
80
ODII
DD
000
F3
F4
F5
F6
F7
F8
F9
F
#3
2$
&
*
70
3
5
7
8
9
< CO
Transcribed Image Text:1. An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 + 0.25x² where V is the shear force and x is length in distance along the beam. We know that V = dM/dx, and M is the bending moment. Integration yields the relationship M = M, + Vdx If Mo is zero and x 12, calculate M using a) trapezoidal rule with 1 m stepsize b) Simpson's 1/3 rule with 1 m stepsize c) Simpson's 3/8 rule with I m stepsize. 2. Please use the following data to calculate f (7) via linear, quadratic, cubic and quartic interpolation. 2.5 3.5 5 6 7.5 10 12.5 15 17.5 f(x) 13 11 8.5 8.2 7 6.2 5.2 4.8 4.8 3. Please use the following dața to calculate f (x = 4.5, y = 3.2) via bilinear interpolation. x = 2 90.00 |x = 8 x = 0 100.00 x = 4 80.00 r= 6 y = 0 70.00 60.00 53.50 y = 2 y = 4 y = 6 85.00 64.49 48.15 50.00 70.00 55.00 48.90 38.78 38.43 30.39 35.03 27.07 25.00 40.00 30.00 20.00 y = 8 40.00 35.00 30.00 4. Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where y(0) = 1. dy = (1 + 2x)/y dx a) Euler's method b) Heun's method without the corrector. 80 ODII DD 000 F3 F4 F5 F6 F7 F8 F9 F #3 2$ & * 70 3 5 7 8 9 < CO
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