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Chapter 27 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- The Gilles & Retzbach model of a distillation column, the system model includes the dynamics of a boiler, is driven by the inputs of steam flow and the flow rate of the vapour side stream, and the measurements are the temperature changes at two different locations along the column. The state space model is given by: x = 0 00 -30.3 0.00012 -6.02 0 0 0 -3.77 00 0 -2.80 0 0 Is the system?: a. unstable b. C. not unstable x+ 6.15 0 0 0 0 3.04 0 0.052 not asymptotically stable d. asymptotically stable -1 u y = 0 0 0 0 -7.3 0 0 -25.0 Xarrow_forwardWrite MATLAB code to perform the following math expression: a) X=7, a=X+2 5 12 2 b) A= 22 L27 4 48 7arrow_forwardThe 2nd order ODE given below models the vertical fall of on Object under the influence of gravity and air friction md²y acceleration -mg + (1/2 Co A Pair) (dy) ² Forcing due logranty Forcing due to air frictionarrow_forward
- For the model defined in Question 1, is the closed loop system with the negative feedback control law? 0 0 0 ;]* X 0 u=-Kx= O a. O b. O c. unstable 0 1 0 asymptotically stable not unstable O d. not asymptotically stablearrow_forwardExample: Sketch the graphs of the following functions. 1. y=sin2x So w nY oy shrin ILYarrow_forward3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0arrow_forward
- 3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx -2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx-2 = 0 u(0) = 1 u(1) = 0arrow_forward3.1-6 DI 3.1-6. Use the graphical method to solve the problem: Maximize Z = 10x + 20x2, subject to -X + 2x, s 15 X1 + x2 < 12, 5x, + 3x s 45 and X 0, x2 2 0. 3.1-11 (a) and (b) only For (a), please specify: (1) Decision variables; (2) Objective function; (3) Constraints. MacBook Proarrow_forwardSolve the initial value problem. y" + 4y' + 20y = 0: y(0) = 2 y (0) = - 3 %3D Chapter 6, Section 6.2, Go Tutorial Problem 12 Find Y(s). 2s + 5 Y(s): s2 + 4s + 20 2s + 5 Y(s) = s2 + 4s + 20 2s – 5 Y(s) : + 4s + 20 2 + 4s + 20 Y(s) 2s + 5arrow_forward
- Using MATLAB to find the maximum.arrow_forward2. An example of a linear decreasing model could be inventory in a warehouse that ships the same number of items each day. We will assume that this warehouse is going out of business, so no new calculators are being sent to the warehouse. Calculators in warehouse Calculators sold per day number of calculators sold per salesperson per day salespeople 2(a). Notice that this model has additional components shown as converters. Based on the titles of the converters, write the equation that must have been used to calculate the flow value in this model. Be sure to include appropriate units. Set the initial number of calculators to 10,000 {calculators}. If nnd that they each sell 15 modelarrow_forward4.17 A source produces independent symbols from an alphabet of three letters. Each source symbols can be A,B or C with respective probability 0.5, 0.25 and 0.25. (a) What is the source entropy H? (b) Find a Huffman code for the individual letters of the source alphabet. What is the average number of bits per symbol for this code? (c) You are asked to design a code for blocks of two symbols from the source at a time. 4.2 To The alphabet for this extended source is of size 9. i woda 819arrow_forward
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