Arizona State University

• MAT 275

• Exercise #1 Part A function LAB04ex1 t0 = 0; tf = 40; %sets the time interval Y0 = [-1;0]; [t,Y] = ode45(@f,[t0,tf],Y0,[]); %called to solve differential Y1 = Y(:,1); Y2 = Y(:,2); figure(1); %Opens the first figure to plot first graph % plots time versus y and v plot(t,Y1,'b-',t,Y2,'r-'); %Plots the graph against time axis grid on; legend('y(t)','v(t)=y''(t)'); ylim([-1.5,1.5]) %creates legend and grid figure(2) %Open second figure to plot second graph % plot the phase plot plot(Y1,Y2);axis square; xlabel('Y_1'); ylabel('Y_2'); %Plots the Phase plot grid on xlim([-1,1]) %sets the window ylim([-1.5,1.5]) [t,Y]; end function dYdt = f(t,Y) y=Y(1); v=Y(2); dYdt = (v: cos(t)-4*v-3*y); end Part B function LAB04ex1 t0 = 0; tf = 40; %The time interval Y0 = [-1;0]; [t,Y] = ode45(@f,[t0,tf],Y0,[]); %Used to solve Differential equation Y1 = Y(:,1); Y2 = Y(:,2); [t,Y] %Output of the matrix end function dYdt = f(t,Y) y= Y(1); v = Y(2); %Defining variables dYdt = [ v; cos(t)-4*v-3*y ];