EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 7, Problem 17P
When trying to find the acidity of a solution of magnesium hydroxide in hydrochloric acid, we obtain the following equation
wherex is the hydronium ion concentration. Find the hydronium ion concentration for saturated solution (acidity equals zero) using two different methods in MATLAB (for example, graphically and the roots function).
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(b)
A beam is subjected to a linearly increasing distributed load. The elastic curve (deflection) is shown
in the figure. The equation to find the maximum deflection is given below. Create a matlab code
where you can calculate the maximum deflection (dy/dx=0) using the bisection method.
Use initial guesses of 1 and 4, L= 6.46 m, E = 59000 kN/cm2, I=35000 cm4, and w0= 2.5 kN/cm.
What will be the value of x (location of maximum deflection) after 14 bisection iteration?
wo
-23 +2L?x³ – L^x)
120EIL
dy
wo
(-5x4 + 6L²a² – Lª)
da
120EIL
Choices
1.4445
O 2.6001
O4.3335
O 2.889
I am trying to find a Direction Cosine Matrix (DCM) for the Euler angle body 1-2-3 sequence. I tried making my own function and using the MATLAB function, but the result is matrices that are not equal to each other. But, if I were to use the 'ZYX' sequence, I would get a matrix that is equal to the transpose of the matrix produced by my function.I mean that transpose(EA123toDCM) = E123toDCM if I changed the sequence to 'ZYX'. I never got two equal matrices. Can you fix my code so I would get two equal DCM matrices for the body 1-2-3 sequence?
Also, for the E123toDCM line, I am using the sequence 'XYZ'. Is that correct or should it be 'ZYX'? I know that that for a DCM of sequence 1-2-3 = R3(theta1)*R2(theta2)*R1(theta3). Is ZYX sequence the same as a 1-2-3 sequence?
EA = [pi/3; -pi/4; -pi/6];EA123toDCM = EA123DCM(EA)
E123toDCM = angle2dcm(EA(1,1), EA(2,1), EA(3,1), 'XYZ')
function [R] = EA123DCM(EA)
theta1 = EA(1,1); theta2 = EA(2,1); theta3 = EA(3,1); R1 =…
Help me solve this USING MATLAB
Chapter 7 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 7 - Divide a polynomial f(x)x47.5x3+14.5x2+3x20 by the...Ch. 7 - Divide a polynomial f(x)=x55x4+x36x27x+10 by the...Ch. 7 - Prob. 3PCh. 7 - 7.4 Use Müller’s method or MATLAB to determine the...Ch. 7 - 7.6 Develop a program to implement Muller’s...Ch. 7 - 7.7 Use the program developed in Prob. 7.6 to...Ch. 7 - Develop a program to implement Bairstows method....Ch. 7 - Use the program developed in Prob. 7.8 to...Ch. 7 - Determine the real root of x3.5=80 with Excel,...Ch. 7 - 7.11 The velocity of a falling parachutist is...
Ch. 7 - Determine the roots of the simultaneous nonlinear...Ch. 7 - 7.13 Determine the roots of the simultaneous...Ch. 7 - 7.14 Perform the identical MATLAB operations as...Ch. 7 - 7.15 Use MATLAB or Mathcad to determine the...Ch. 7 - A two-dimensional circular cylinder is placed in a...Ch. 7 - 7.17 When trying to find the acidity of a...Ch. 7 - Consider the following system with three unknowns...Ch. 7 - 7.19 In control systems analysis, transfer...Ch. 7 - Develop an M-file function for bisection in a...Ch. 7 - 7.21 Develop an M-fi le function for the...Ch. 7 - 7.22 Develop an M-fi le function for the...Ch. 7 - Develop an M-fi le function for the secant method...Ch. 7 - Develop an M-file function for the modified secant...
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- I am trying to find a Direction Cosine Matrix (DCM) for the Euler angle body 1-2-3 sequence. I tried making my own function and using the MATLAB function, but the result is a matrix that is transpose of each other. I mean that transpose(EA123toDCM) = E123toDCM. Why is that? Also, for the E123toDCM line, I am using the sequence 'ZYX'. Is that correct or should it be 'XYZ'? I know that that for a DCM of sequence 1-2-3 = R3(theta1)*R2(theta2)*R1(theta3). Is ZYX sequence the same as a 1-2-3 sequence? EA = [pi/3; -pi/4; -pi/6];EA123toDCM = EA123DCM(EA) E123toDCM = angle2dcm(EA(1,1), EA(2,1), EA(3,1), 'ZYX') function [R] = EA123DCM(EA) theta1 = EA(1,1); theta2 = EA(2,1); theta3 = EA(3,1); R1 = @(a)[1 0 0 ; 0 cos(a) -sin(a); 0 sin(a) cos(a)]; R2 = @(a)[cos(a) 0 sin(a) ; 0 1 0 ; -sin(a) 0 cos(a)]; R3 = @(a)[ cos(a) -sin(a) 0; sin(a) cos(a) 0;…arrow_forwardCan you help me code the algorithm into MATLAB? The delta zero, delta one and so forth are equal to the determinats of a 3x3 matrix made of the three vectors.arrow_forwardplease answer question 3 , 5, 7 in full detail explanationarrow_forward
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