MAT275_Matlab_lab4 - Alicia Kent – Lab 4 Exercise 1%A...

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Alicia Kent – Lab 4 Exercise 1 %A LAB04ex1 %B - The blue plotted line, y(t), had local maximums at: % t = .0047, 7.23, 13.66, 19.93, 26.21, 32.49, and 38.78 % The red plotted line, y'(t), had local maximums at: % t = .52, 5.77, 12.09, 18.42, 24.71, 30.99, 37.28 %C % The long term behavior of y oscillates by looking at the graph. %D % The long term behavior of the graph did not change. This is because only % the initial conditions were changed. So only the beginning of the graph % looks different but long term the graph still oscillates. LAB04ex1.m file: function LAB04ex1 t0 = 0; tf = 40; y0 = [1.5,5]; % changed from "[-1,0]" to "[1.5,5]" for Exercise 1 Part C [t,y] = ode45(@f,[t0,tf],y0,[]); [t,y]; %supressed output to see local maximums u1 = y(:,1); u2 = y(:,2); % y in output has 2 columns corresponding to u1 and u2 figure(1); plot(t,u1, 'b-+' ); hold on plot(t,u2, 'ro-' ); legend ( 'v(t)' , 'v(t)=y''(t)' ) ylim([-1.5,1.5]) grid figure(2) plot(u1,u2); axis square ; xlabel( 'y' ); ylabel( 'y=y''' ); % plot the phase plot ylim([-1.5,1.5]) xlim([-1,1]) grid end %---------------------------------------------------------------------- function dYdt= f(t,Y) y=Y(1); v=Y(2); dYdt = [v; cos(t)-4*v-3*y]; end
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2 Alicia Kent Exercise 2 %A LAB04ex2 %B % When the y^2 was added to the IVP, it made the sol. graphs oscillate with % bigger max and min values. The beginning of the graph was
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