1. An 11-m beam is subjected to a load, and the shear force follows the equationV(x) = 5 + 0.25x²where V is the shear force and x is length in distance along the beam. We know that V = dM/dx, and Mis the bending moment. Integration yields the relationshipM = M, +VdxIf Mo is zero and x 12, calculate M usinga) trapezoidal rule with 1 m stepsizeb) Simpson's 1/3 rule with 1 m stepsizec) Simpson's 3/8 rule with I m stepsize.2. Please use the following data to calculate f (7) via linear, quadratic, cubic and quarticinterpolation.2.53.5567.51012.51517.5f(x)13118.58.276.25.24.84.83. Please use the following dața to calculate f (x = 4.5, y = 3.2) via bilinear interpolation.x = 290.00|x = 8x = 0100.00x = 480.00r= 6y = 070.0060.0053.50y = 2y = 4y = 685.0064.4948.1550.0070.0055.0048.9038.7838.4330.3935.0327.0725.0040.0030.0020.00y = 840.0035.0030.004. Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25where y(0) = 1.dy= (1 + 2x)/ydxa) Euler's methodb) Heun's method without the corrector.80ODIIDD000F3F4F5F6F7F8F9F#32$&*7035789< CO

Since the second question is independent of the first question. As per the guidelines I am answering…

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 1 m stepsize.

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 1 m stepsize.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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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