hw25 - w=2.0; dy = zeros(2,1); % a column vector dy(1)=y(2);

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w=.5 w=1
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w=1.5 w=2
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%example numerical solution of 1st order ODE %dy/dt=-k(u-T0+T1cos(wt)), y(0)=40 y0=40; %initial value tspan= [0:1:400]; %creates vector of times for plotting [t,y]=ode23( 'function_hw4' ,tspan,y0); %computes numerical solution and %returns t and y vectors hold off %starts new plot plot(t,y, 'o' ) %plots t vs y with open symbol %compare with analytical solution c= 40; w= pi/66; % ID number ends in 66 k= 0.02; T0= 20; T1= 40; yanaly= T0 - k*T1*((k*cos(w*t))+w*(sin(w*t))/(k^2+w^2)) + 40*exp(-k*t); hold on %next plot overlays prior plot plot(t,yanaly) %plots analytical solution w/ solid line xlabel( 't' ) ylabel( 'y' ) figure R = zeros(1,4); w = zeros(1,4); R(1) = 1.125; R(2) = 1.9; R(3) = .8; R(4) = .34 w(1) = .5; w(2) = 1; w(3) = 1.5; w(4) = 2; plot(w,R) xlabel( 'w' ) ylabel( 'R' ) ______________________________________________________ function dy=derivative(t,y)
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Unformatted text preview: w=2.0; dy = zeros(2,1); % a column vector dy(1)=y(2); dy(2)=cos(w*t)-.2*y(2)-y(1)-.2*y(1)^3; w=.5 w =1 w=1.5 w=2 %3.8.25.c %numerical integration of 2nd order equation %u"+.2u'+u+ .2u^3=cos(wt), u(0)=0, u'(0)=0 %from 0 to 70, with plotting steps of 0.1 time units u0=0; v0=0; Y0=[u0 v0]; %initial conditions Tspan=[0:.1:150]; %times for plotting [T,Y]=ode23( 'derivative2' ,Tspan,Y0); figure(1) plot(T,Y(:,1)) xlabel( 't' ) ylabel( 'u' ) figure R = zeros(1,4); w = zeros(1,4); R(1) = 1.825; R(2) = 2.80; R(3) = 2.10; R(4) = 0.62; w(1) = .5; w(2) = 1; w(3) = 1.5; w(4) = 2; plot(w,R) xlabel( 'w' ) ylabel( 'R' ) ______________________________________________________ function dy=derivative2(t,y) w=2; dy = zeros(2,1); % a column vector dy(1)=y(2); dy(2)=cos(w*t)-y(1)-.2*y(1)^3;...
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hw25 - w=2.0; dy = zeros(2,1); % a column vector dy(1)=y(2);

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