Problem 1/MatlabGrader (15 points, CCO #8) Develop a Matlab function myRK3 that performs a single step of a third-order Runge-Kutta method for the ODE dy dx = f(x, y). The RK coefficients are given in the following so-called Butcher tableau using the variable names from the text book/lecture 0 1/2 1/2 a1 a2 b21 аз b31 b32 C1 C2 C3 3/4 0 3/4 2/9 1/3 4/9 (1) (2) As input the function shall take the function f, the current independent variable xi and dependent variable yi corresponding to the current solution point (xi, yi) and the step size h. As output the function shall give the new independent variable x and dependent variable y corresponding to the new solution point (x+1, Yi+1). Note, to pass the Matlab Grader tests, you must use global kl k2 k3 slope; inside your function and use these variable names for the respective components of the RK method. Remove this global statement after submission to Matlab Grader for the following problems. Required submission: ☐ well commented function source code submitted to Matlab Grader Problem 2/MatlabGrader (10 points) A water tank of radius R with two outlet pipes of radius r₁ and r2 installed at heights h₁ and h₂ is mounted in an elevator moving up and down causing a time dependent acceleration see Fig. 1. g(t)goa, cos(2π fgt), R 1 H Figure 1: Water tank inside an elevator The height of water h(t) in the tank can be modeled by the following ODE, where dh dt (3) f(t)-p√2g(t) (r√✓√max(0, h − h₁) + r√//max (0, h - h2) PTR² (4) f(t)=c[2+ sin (2π fit + cos(2π f2t))] (5) models the inflow into the tank. Note that the cos is within the sin in f(t). Write a Matlab function myRHSE8 that takes as input the current time t and height h and returns the scalar value rhs of the right-hand-side of Eq. (4). Use global variables for all parameters used in the right-hand-side, i.e., for go, ag, fg, p, R, r₁, r2, h1, h2, c, f1, f2 use go, ag, fg, rho, R, rl, r2, h1, h2, c, f1, and £2, respectively. The max appearing in Eq. (4) is returning the larger of the 2 scalar argument values and is implemented in Matlab as the max function, e.g., max(0, h - h₁) is simply max (0,h-h1). Required submission: ☐ well commented function source code submitted to Matlab Grader Problem 3/MatlabGrader (10 points, CCO #8) For the case described in problem 2 with go = 9.81m/s², ag = 4m/s², fg = 0.0017Hz, p = 1000kg/m³, R = 1.8m, r1 = 0.09m, r2 = 0.04m, h₁ = 0.13m, h₂ = 0.2m, c = 31 kg/s, f₁ = 0.013Hz, and f2 = 0.024Hz, calculate the height of water in the tank at t=2500s using the third-order Runge-Kutta method of Problem 1 with a step size of At = 10s if the initial height of water in the tank is 0.35m. Store the value of the height of water in the tank at t=2500s in the scalar variable answer. In your script, define all the above given parameters as global variables. MatlabGrader will provide working copies of both my RK3 and myRHSE8 so these do not need to be part of your MatlabGrader submission for this problem. Required submission: ☐ well commented script source code submitted to Matlab Grader Problem 4 (25 points, CCOs #1 & #8) For the case described in problems 2 and 3, calculate the height of water in the tank at t =2500s to within 10-7m using either the third-order Runge-Kutta method of Problem 1, or, for a 10 point deduction, the classical RK-4 method. Outside of your code, report the method you have chosen to solve this problem, the final step size At employed and all supporting evidence that your result has the required accuracy. Note that for full credit it is not sufficient to only show that the estimated error is below the requested threshold, but you must also show that your chosen method converges as expected. Report h(t =2500s) as a floating point number in engineering notation with at least 10 mantissa digits. Required submission: Name of RK method chosen (including this name in code is not sufficient) h(t=2500s) (at least 10 digits reported), employed At, and all supporting evidence ☐ printout of any new functions coded that were not part of previous exams/homework; printout of script used to solve this problem (can be a combined script);

Can 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.

Given the trasnfer function G(s) numerator and denominator coefficients for Matlab code should be: O s³+2s+1 2s4+2s²+1' the num= [1 0 2 1] and den=[2 020 1] O num=[1 2 1] and den=[2 0 2 1 1] O num=[1 2 1] and den=[2 2 1] O num=[1 0 2 1] and den=[2 2 0 1]

Problem 1 (15 points) (Core Course Outcome 5)/MatlabGrader Write a function mySecond Derivative Order 3 that calculates the second derivative d²y/dx² of a data set (x, y) with at least third order accuracy at each data point. The data is equidistant in x with spacing h. The function input shall be ⚫y: one-dimensional column vector of y values ⚫h: scalar value of spacing h The function output shall be • d2y: column vector of the same size as y containing d²y/dx² Calculate d²y/dx² using only the following formulas that use the nomenclature of Table 8-1 and the lecture notes, but are different from the formulas listed there: f" (xi) 164f(xi) — 465f(xi+1) + 460ƒ (xi+2) − 170ƒ (xi+3) + 11f (xi+5) + O(h³) = 60h2 56f(xi−1) − 105f(xi) +40f(xi+1) + 10f(xi+2) − f(x+4) + O(h³) 60h² −5f(xi−2) +80f(xi−1) − 150f(xi) + 80f(xi+1) − 5ƒ(xi+2) (1) f"(xi) = (2) f"(xi) = +0(h) (3) 60h2 f"(xi) -2f(x-4)+5f(xi-3)+50f(xi-1) — 110f(xi) +57f(xi+1) = +0(h³) (4) 60h² f"(xi) = 57f(x-5) 230f(xi-4) + 290 f (xi-3)-235…

MATLAB...Hand written plzzzz asap....FAST PLZZZZZZZZZZZ

Consider the following Initial Value Problem (IVP) dy /at = -t * sin (y); y(t = 0) =1 Solve for y(t=0.5) using a) Forward Euler method with At = 0.25. (Solve by hand) Develop a Matlab script that solves for y (t = 5) using Forward Euler method. Use the time step levels given below and plot t vs y in the same plot. Include the plot with the right format (axis labels, legends, ...) in your solution sheet and include your Matlab script in the solution as well. i) At = 0.25 ii) At = 0.125 b) Backward Euler method with At = 0.25 (Solve by hand)

Please follow the instructions and the requirements according to the pictures above and I kinda need the solution quickly. The language of the code is in Matlab, thank you in advance.

I am having trouble with the folloiwng MATLAB code. I am getting an error that says "unrecognized function or variable 'numericalPropogatorOptions". I have the aerospace toolbox and the aerospace blockset added. what add on do I have to download to use that function. How do I make this code work?     % Define Keplerian Elements a = 29599.8; e = 0.0001; i = 0.9774; Omega = 1.3549; w = 0; M = 0.2645; [RECI, VECI] = Kepler2RV(a, e, i, Omega, w, M); initialState = [RECI * 1e3; VECI * 1e3]; % Initial position (m) and velocity (m/s)   % Define constants mu = 3.986004418e14; % Gravitational constant (m^3/s^2) earthRadius = 6378.1363 * 1e3; % Earth radius in meters j2 = 1.08263e-3; % J2 perturbation coefficient   % Define propagator options propOptions = numericalPropagatorOptions('CentralBody', 'Earth', ... 'GravitationalParameter', mu, ... 'InitialState', initialState, ... 'OutputTimeStep', 300); % Output every 300 seconds   % Add perturbations addGravityModel(propOptions, 'Degree', 2,…

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;…

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 =…