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Question Sailboat Mast The following equation be used to model the deflection sailboat mast subject b wind force: dy-56-(2-2) 2EI where Eis the modulus of clasticity. Lthe mast length, Ithe second moment of area and f(z) is the wind force depending the height andi given by: f(z)= Calculate the deflection of the mast using the 4th order Runge Kutta method with y=0 and "=0 ==0 Perform the first analysis with divisions of the length Ltc define the step (see the table below for your assigned value f n). Repeat the analysis with twice the number of divisions (i.e. 2n divisions) and produce graph of the deflection and curvature the height for the two cases. Number of Data Set E(N/m²) ((m) L(m) Divisions, n 1.08E+OS 0.05 29 1.34E+OS 0.03 42 1.18E+OS 0.04 41 1.01E+OS 005 1.25E+OS 0.06 10 6 1.32E+OS 0.07 41 1.50E+OS 0.08 19 1.05E+OS 0.04 39 1.10E+O8 0.05 14 10 1.44E+O8 0.06 35 10 1.05E+OS 0.04 40 12 1.10E+OS 0.06 36 1.05E+OS 0.07 28 14 1.25E+OS 0.05 30 Source Numerica Mcthods for Engineers Chapra Question Hanging Cable It can be shown that the curve y(x) an inextensible flexible homogeneous cable hanging between two fixed points obtained by solving the following equation: where the constant depends on the weight This curve called a "catenary ("chain in Latin) Find and plot y(x). assuming given value for k and those fixed points are (-1,0) and (1,0) in a vertical ry-plane. using the 4th order Runge Kutta method with step of 0.025. N.B. you should use reasonable estimate for the initial slope and modify the spreadsheet until the solution is correcti.c the slope the midpoint zero. Data Set 10 0.6 os 1.3 1.3 15 07 1.2 11 1.45 12 1.25 1.15 14 09 Source Numerica Methods for Engineers Chapra Question Carbon Monoxide Concentrations in a Restaurant Qins Cine Cing Qouts Qinx + Kitchen Eating Area - Qouta Grill Load EL Wagill Overhead view oftwo a restaurant Th volumetric mising The gillloads add carbon momoride airflow Indoor pollution deals with air contamination in closed spaces such a the restaurant shown here. Suppose you are designing ventilation system for the restaurant which consists of kitchen larger cating areal The kitchen has source of carbon monoxide from faulty grill The differential equation describing the variation of carbon monoxide with time in the kitcheni performing mass balance where Cx deating area respectively the diffusive between the two while Qouts and Qoute are determined by calculation You should for the area and then solve both equations with the Runge method should produce plot of the temporal variation of carbon monoxide You should assume the initial values of Cgand C, Cing Cing Data St Wgrill 500 100 600 120 550.0 100 400.0 800.0 20 1000.0 25 750.0 20 500.0 25 600.0 120 30 650.0 400.0 550.0 580.0 14 680.0 125 30 Vkinches V1=10x 8, 3.5 280m V¿=10x 24x3.5=840m 25m'/h Source Numerical Methods for Engineers Chapra

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h = 1; % time step
T = 0:h:50; % timespan
n = length(T);

C = [0, 0]; % initial conditions

Ck = zeros(n,1);
Ce = zeros(n,1);

for i=1:n-1
    t = T(i);
    k1 = h*f(t,C);
    k2 = h*f(t+h/2, C+k1/2);
    k3 = h*f(t+h/2, C+k2/2);
    k4 = h*f(t+h, C+k3);
    C = C + (k1+2*k2+2*k3+k4)/6;
    Ck(i+1) = C(1);
    Ce(i+1) =...

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