Symbolic Math Toolbox: Unable to find explicit solution, Line 317

Before anything, I'm definitely a beginner using MATLAB, so there may be something obvious wrong with my code.

Using the below code, I receive an error, but I'm not really sure why

The values in the M matrix were obtained by hand (dont think theres a problem, but there might be, I've checked it over several times)

I've taken out the for loop, reduced the values of a (to just .1 for the sake of trying to just get an initial solution), changed variable names, and tried to solve for other variables (namely L, just to try something else), and uninstalled all other add-ons.

The end goal is to get (k) for each (a) value in terms of (L)

This is using MATLAB R2020B, for academic use, Symbolic Math toolbox

Thank you for your time and assistance

Mike

P.S. This is for homework, the initial S value changes with every student (1 through 49).

P.P.S. For some context, this is for my MechEng class that goes over the buckling of columns (for this question) and deflections of beams.

OldCode:

clc, clear, close all
s=13
sa=sqrt(s+1)
a=.1:.1:.9
syms L k
for i=1:9
    M=[(-sin(k*a(i))) (sin(k*sa*a(i))) (cos(k*sa*a(i))); (-k*cos(k*a(i))) (sa*cos(k*sa*a(i))) (-sa*sin(k*sa*a(i)));(0) (sin(k*sa*L)) (cos(k*sa*L))]
    detM=det(M)
    c=solve(detM,k)
end

OldError message:

 
Warning: Unable to find explicit solution. For options, see help. 
> In sym/solve (line 317)
In Untitled (line 9) 
 
c =
 
Empty sym: 0-by-1

NewCode:

clc, clear, close all
s=13;
sa=sqrt(s+1);
syms L k
a=.1*L;
M=[(-sin(k*a)) (sin(k*sa*a)) (cos(k*sa*a)); (-k*cos(k*a)) (sa*cos(k*sa*a)) (-sa*sin(k*sa*a));(0) (sin(k*sa*L)) (cos(k*sa*L))];
detM=det(M)
c=solve(detM,k)

NewError message:

 
Warning: Unable to find explicit solution. For options, see help. 
 
c =
 
Empty sym: 0-by-1
 
>> 

Edit1: Some grammar mistakes I noticed

Edit2: Slightly changed the code due to me making an oopsie in my hand calculations, error remains

Edit3: Changed the code (again) due to misunderstanding what some of the variables mean, error remains

Edit4: Change the code (again) to take out the for loop to make it easier to troubleshoot, error 317 went away, but still wont find the solution

[Walter Roberson]

recommend that you use vpasolve instead of solve

[Michael Huber]

Thanks for the suggestion!

I'm not exactly sure how I would solve using vpasolve, since I need K in terms of L, I thought vpasolve just tried numbers until it got a correct answer

Do I need to take my system of equations out of the determinant and set it into a new array?

[Michael Huber]

As an update to (attempt) to use vpasolve, I made this code based on the original code, it returned no errors, but said code returned:

k=0

L=0

Which are very obviously not correct (L is any arbitrary value for length, and k in this case represents the load value required for buckling divided by constants)

clc, clear, close all
s=13;
sa=sqrt(s+1);
syms L k
a=.1*L;
M=[(-sin(k*a)) (sin(k*sa*a)) (cos(k*sa*a)); (-k*cos(k*a)) (sa*cos(k*sa*a)) (-sa*sin(k*sa*a));(0) (sin(k*sa*L)) (cos(k*sa*L))];
detM=det(M)
c=vpasolve(detM,[k L])

Once again, im not exactly knowledgeable in MATLAB so I may be incorrectly using vpasolve

[Walter Roberson]

You are not going to be able to find a solution.

There are an infinite number of solutions for k in terms of L.

Pick an L such as 1 and plot out the equation over a small range such as 1 to 20.

[Michael Huber]

Ah ok

Seems I was going about this the wrong way then.

Thanks for your help!

Mike