Write a Simulink program in MATLAB to find Model the differential equation x"(1) = x'(t)x(t)– 2x(t) + u(t) Where u(t) is a square wave with an amplitude of 1 and a frequency of 1rad/sec.
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- Write a Simulink program in MATLAB to find Plot the following functions y(t) = sin-'(t) Using Ramp functionWrite program in matlab for function Taylor's series of ln(x)using x0=1Solve the following problems in Octave or Matlab 1. Write an M-function function [x,iter,err]-Jacobi(A,b,tol,kmax) Then, test it for the solution of the linear system Ar= b with 1 toplit([11 0 0 0 0]) and b chosen so that the exact solution of the system is z = [2.2.2.2.2.2]T. The output parameters are: x the solution vector; iter the number of iterations and err the relative errors among iterations. 2. Do the same for Gauss-Seidel 3. Again, with same data of the first exercise, write an M-function: function (x,iter,err]-SOR(A.b.tol.kmax,omega); that implements the relaxation method. Notice verify that this function can be used also as Gauss-Seidel method when omega = 1 4. Without executing any code, verify if the Jacobi method couverges if the case when, given r = [1.1,5.2.2.5.3).we want to solve the system V'a = y, where = vander(r) and y = sin(x). The solution of the system, if exist, will give the coefficients of the interpolating polynomial of degre 1 of the sinus function at the…
- Simplify the Boolean function F(w,x,y,z) = (0,1,2,4,5,6,8,9,12,13,14)Simplify the following Boolean function , using three- variable maps: d) F(x,y,z) = Σ (3,5,6,7)With the MATLAB editor, please make a script m-file for the following: Simple harmonic motion is a mass connected at the end of a lossless spring. The position of the spring is defined by: y(t) = c1cos(ωt) + c2sin(ωt) Where The kinetic energy of the mass is defined by: And that c1 = 0.172 m, c2 = 0.012 m, k = 3.2 N/meter and m = 0.32 kgFor values of t from 0 to 8.25 sec in increments of 0.05 secMake variables c1, c2, k and m and assign valuesPlease Calculate the value of omega in rad/secFind the values of y in cm and KE in JoulesUsing subplots make two side by side plots within one figure:Display the results on a x-y scatter plot With t the independent variable plotted on the x axisAnd y the dependent variable plotted on the y axisInclude units within the labels Show the results on a x-y scatter plot With t the independent variable plotted on the x axisAnd KE the dependent variable plotted on the y axisInclude units within the labels
- 2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…Reduce this term into normal from, if it exists (show your working):(λx.((λz.zwz)(((λxyx.y)(λx.y)(λy.x))((λx.xx)(λy.yyy)))))t2- Let be f(t) a real, periodic function satisfy f(-t)= -f(t), The general form of the Fourier series representation would be: a- f(t) = 1 bnsin nw,t b- f(t)= ao+n=1 an cos nwot c- f(t) = -1 an cos nwot 100 n= 100 d- f(t) = Eno bn sin nwot