ODE plot with 2nd order diff eqs

I wanted to check to make sure I am creating the correct graph for problem 1 of the attached project file. It is similar to a previous problem I had to do , so I used that code and just changed the equation and conditions to match this problem.

 Fp = @(t,x,w) [x(2); 10*cos(t.*w)-x(1).*4-x(1).*5];       % Spring ODE
ww = [0, 0.5, 1, 2, 4, 8, 16];                                     % ‘epsilon’ Vector
ts = linspace(0,80, 500);                            % Time Vector
for k1 = 1:length(ww)
    [~, x{k1}]=ode45(@(t,x) Fp(t,x,ww(k1)), ts, [0,1]);
end
figure(1)
for k1 = 1:length(ww)
    subplot(length(ww), 1, k1)
    plot(ts,x{k1})
    legend(sprintf('\\epsilon = %.1f', ww(k1)))
    grid
    axis([xlim    -5  +5])

[Torsten]

Your equation to be solved and your initial conditions are not consistent with project2.pdf.

Check again.

Best wishes

Torsten.

Answer 1

[Star Strider]

The problem is that the loop code isn’t updated to match your new ODE. (Your ODE code and ode45 call are correct.)

Use this loop instead of the old one:

figure(1)
for k1 = 1:length(ww)
    subplot(length(ww), 1, k1)
    plot(ts,x{k1}(:,1))
    hold on
    legend(sprintf('\\omega = %.1f', ww(k1)))
    grid
    axis([xlim    -2  +2])
    xv = x{k1}(:,1);
    zxix = find((xv.*circshift(xv, [1 0])) <= 0);               % Approximate Zero-Crossing Indices
    if length(zxix) > 2
        ixrng = max(1,zxix(3)-1):min(zxix(3)+1,length(ts));     % Index Range
        tzx{k1} = interp1(xv(ixrng), ts(ixrng), 0);             % ‘tx’ Values At Zero-Crossings
        plot(tzx{k1}, zeros(size(tzx{k1})), 'bp')               % Plot Zero Crossings
    end
    hold off
end
xlabel('Time')