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  1. % script for excercise 1 of case study 1 for EMATH171
  2. % in this script we solve for V using newtons method repetating untill we
  3. % have a tolerence of 0.0001
  4. clear
  5. clc
  6. close all
  7.  
  8. % Coefficients for the function and its deriviative
  9. m = 1000;
  10. g = 9.81;
  11. theta = 0.25 * pi;
  12. coff_friction = 0.2;
  13. a = 1;
  14. b = 100 * pi;
  15. rgb = 20;
  16. R = 0.5;
  17.  
  18.  
  19. % functions
  20. j = @(v) (m .* g .* (sin(theta)) .* v) + (coff_friction .* m .* g .* (cos(theta)) .* v);
  21. % motor shaft rotation speed
  22.  
  23. k = @(v) (a .* ((b .* ((rgb .* v) / R)) - (((rgb.^2) * (v.^2))/(R.^2))));
  24. % power output
  25.  
  26. f = @(v) j(v) - k(v);
  27. % origional function
  28.  
  29. g = @(v) (m .* g .* (sin(theta))) + (coff_friction .* m .* g .* (cos(theta))) - (a .* ((b .* (rgb / R)) - ((2 .* (rgb.^2).* v)/(R.^2))));
  30. % deriviative
  31.  
  32. h = @(old_x) old_x - ((f(old_x))/(g(old_x)));
  33. % newtons method propper
  34.  
  35. % Coefficients for newtons method
  36.  
  37. N = 200;
  38. % maximuim amount of repetitions, unlikley to actualy reach this value
  39.  
  40. x = 2;
  41. % initial guess
  42.  
  43. tol = 0.0001;
  44. %tolerence of diffrence between iterations
  45.  
  46. out_array = [x];
  47. % output array of the results of newtons methods approximations
  48.  
  49. error_array = [abs(f(x))];
  50. % array of the error
  51.  
  52. delta_array = [];
  53. % array of change between iterations
  54.  
  55. counter = 0;
  56. % tracks number of iterations
  57.  
  58. % Newtons method implementaion
  59.  
  60. for item = 1:N
  61.     old_x = x; % saving old x
  62.     delta_array(item) = (x);
  63.     x = h(x); % creating new x
  64.     counter = counter + 1;
  65.     out_array(item+1) = x;
  66.     error_array(item+1) = abs(f(x));
  67.     delta_array(item) = abs(delta_array(item)- x);
  68.     if and((abs(f(x))<tol),(abs(x-old_x)<tol))
  69.         counter = counter - 1;
  70.         break
  71.     end
  72. end
  73.  
  74. % display
  75. figure
  76. hold on
  77. x_actual_array = [0:0.1:5];
  78. plot (x_actual_array, j(x_actual_array))
  79. plot (x_actual_array, k(x_actual_array))
  80. hold off
  81. x
  82. counter
  83. out_array
  84. error_array;
  85. delta_array;
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