Solve Equation and Plot it

Hello, i have the follwing equation:

0 = 0.5*alpha*(w(1)*f_1-w(2)*f_2)^2+p(1)*f_1+p(2)*f_2+skalar- AF_z

which i want to write like f_2 = ... and plot after f_2 for f_1 = linspaces(0,20).

At this moment we already know that alpha = 0.4207, skalar = 4.5375, AF_z = 5,9796, w = [0.77,0.23], p = [-0.9851,0.5243]. So the only values we do not know is f_1 and f_2

So i started like this:

syms f_1 f_2
g = 0.5*alpha*(w(1)*f_1-w(2)*f_2)^2+p(1)*f_1+p(2)*f_2+skalar- AF_z;
x = solve(g,f_2);

As there is a root (+/- sqrt), when reshaping the equation to f2 =..., the structure of x is 2x1 sym.

And now i want to plot for all f_1 betweem 0 and 20 the f_2 values.

I know that i need to use fplot.

The solution should look like the pic.

Thank you already for the help

Answer 1

[Star Strider]

The result ie not exactly the same as the plot in the original question, however it is close —

alpha = 0.4207; 
skalar = 4.5375; 
AF_z = 5.9796; 
w = [0.77,0.23]; 
p = [-0.9851,0.5243];

syms f_1 f_2
g = 0.5*alpha*(w(1)*f_1-w(2)*f_2)^2+p(1)*f_1+p(2)*f_2+skalar- AF_z;
x = solve(g,f_2)

x = 

figure
fplot(x, [0 10])
grid
xlim([0 20])

The dashed vertical line denotes a singularity at .

.

[Daniela Würmseer]

Thank you

[Star Strider]

As always, my pleasure!

Answer 2

[John D'Errico]

Easy peasy. Essentially one line of code once you define the various constants.

syms f_1 f_2
alpha = 0.4207;
skalar = 4.5375;
AF_z = 5.9796; % You wrote 5,9796 but note that numbers in matlab are written with decimal points, not commas.
w = [0.77,0.23];
p = [-0.9851,0.5243];
fimplicit(0 == 0.5*alpha*(w(1)*f_1-w(2)*f_2)^2+p(1)*f_1+p(2)*f_2+skalar- AF_z,[-5 10 -10 20])

The exact shape will of course depend on the exact constants used. It appears the constants were subtly different to create the figure you posted.

[Daniela Würmseer]

Thank you.