Using a range as an input value in symbolic equations

Hello,

I would like to use a range of value, instead of a specific value, as one of inputs in a symbolic equation, but getting errors, and hope I can get help.

Here is a script I wrote:

syms A omega x positive

% Parameters
alpha = 6*pi;
beta = 25;
omega = 0.1;
A = [0 0.5];
% A = 0.1;


eqn = omega == sqrt((1 + (2*A.*x).^2) ./ ((1-x^2)^2 + (2*A.*x).^2)) ;
X = vpa(solve(eqn,x));


k = beta * alpha^2 / X.^2;
c = 2 .* A .* sqrt(k.*beta)


figure();
fplot(k,A)
hold on
fplot(c,A)

What I am trying to do is:

1. solve the equation (eqn) for x and return only positive x (X)
2. calculate k and c with a calculated X and given variables
3. plot k and c value with respect to A

It returns a correct k and c values when I set A a single value, but when I set this a range of value I get the following error:

Error using  .* 
Array sizes must match.

When I put A below " X = vpa()" line, it plots right k values, but not c. (it should print around c= 28 when A = 0.1, but gives me around c= 140 in the graph, and now c has a 1x2 system)

I would appreicate your help.

Answer 1

[Dyuman Joshi]

You get the error because A is 1x2 and x is 1x1 and you can not multiply 1x2 to 1x1. Now you would think of changing the order, but in that case, the system will have 2 equations with 1 variable, which is not consistent.

You can either

1 - Use a loop, or,

2 - Define x as 1x2 sym, and proceed further

syms x positive

whos x

  Name      Size            Bytes  Class    Attributes

  x         1x1                 8  sym                

% Parameters
alpha = 6*pi;
beta = 25;
omega = 0.1;
A = [0 0.5];
% A = 0.1;

%Loop
%Assuming you are sure that only 1 positive root exists 
%for each element of A
for k=1:numel(A)
    X(k) = vpasolve(omega == sqrt((1 + (2*A(k)*x).^2)./((1-x^2)^2 + (2*A(k)*x).^2)));
end
X

X = 

k = beta*alpha^2./X.^2

k = 

c = 2.*A.*sqrt(k.*beta)

c = 

figure();
fplot(k,A)
hold on
fplot(c,A)

[GradyGr]

Hello Dyuman, thank you so much. Your solution solved my issue!