Plotting Answers to dsolve

Trying to get the answers to show up on plot

Code:

for w = 1.3, 1.5, 1.8, 1.9
    dsolve('2*D2h + 8*h = 5*cos(w*t)')
    figure; plot(w); axis equal; axis([0 40 0 40])
end

Doing this is giving me a plot but nothing is actually plotted on the graph.

Answer 1

[Star Strider]

Your function may be only a function of time (guessing here because you didn’t specifically state that in your code), however the the integrated function is of both ‘w’ and ‘t’, so if you want to plot it, you have to plot it as a function of both.

This works. I leave it to you to determine if it produces the results you want:

syms h(t) w
Dh(t) = diff(h);
h_sol = dsolve(2*diff(h,2) + 8*h == 5*cos(w*t), h(0) == 0, Dh(0) == 0);     % Integrate
h_sol = simplify(h_sol, 'steps', 20);                                       % Simplify
h_fun = matlabFunction(h_sol);                                              % Create Anonymous Function

h_fun = @(t,w)(sin(t.*w.*(1.0./2.0)).^2.*5.0-sin(t).^2.*5.0)./(w.^2-4.0);   % Copied & Pasted For Convenience

w = [1.3, 1.5, 1.8, 1.9];
t = linspace(0, 1, 25);

[W,T] = meshgrid(w,t);

figure(1)
meshc(T,W,h_fun(T,W))
grid on
xlabel('\bft')
ylabel('\bfw')
zlabel('\bfh(t,w)')

The meshgrid call is necessary if you want to calculate and plot it correctly.

[Bob]

I do not think this is what I wanted. Here is the question: equation: 2h" +8h=0. Let's hook the object up to a motor im-parting an external force of 5cos(wt). Use dsolve to get formulas for the displacement when w = 1.3, 1.5, 1.8, 1.9. Graph your formulas on the interval [0;40].

[Bob]

This is my updated code:

for w = 1.3, 1.5, 1.8, 1.9
    f = dsolve('2*D2h + 8*h = 5*cos(w*t)');
    t = 0:1:40;
   figure; plot(t,f) 
end

But it is saying non numeric data is not supported.

[Star Strider]

You weren’t specific about what you wanted. My symbolic code provides the correct solution (conventionally assuming zero initial conditions), and produces an anonymous function for the solution, so I won’t repeat it here.

If you want a family of curves, change the plotting part of the code to:

h_fun = @(t,w)(sin(t.*w.*(1.0./2.0)).^2.*5.0-sin(t).^2.*5.0)./(w.^2-4.0);   % Copied & Pasted For Convenience

w = [1.3, 1.5, 1.8, 1.9];
t = linspace(0, 40, 250);

[W,T] = meshgrid(w,t);

figure(1)
plot(t, h_fun(T,W))
grid on
xlabel('\bft')
ylabel('\bfh(t,w)')
lgndcell = regexp(sprintf('w = %.1f\n',w), '\n','split');
legend(lgndcell(1:end-1), 'Location','NW')

That should do everything you want: