How do I plot and return the values of multiple intersections between a function and zero?

Hello,

I need to find the intersection between the det_a function and zero, return the values, and plot the intersections. Here's what I did so far

x = linspace(0,18,1000);
det_a = sin(x).*cosh(x) - cos(x).*sinh(x);
zr = zeros(size(x));

figure
plot(x,det_a,x,zr,'--')
grid on
ylim([-10 10])
xlabel('\betal')

The plot can be seen here:

I haven't found any easy method of doing this, I've tried using the find and intersect functions but they only return one value. Any help would be appreciated, thanks in advance!

Answer 1

[Alan Stevens]

Here's one possibility (though you get repeated results for the roots!):

det_a = @(x) sin(x).*cosh(x) - cos(x).*sinh(x);
x=0:18;
zr = zeros(1,numel(x));
for i = 1:numel(x)
    zr(i) = fzero(det_a, x(i));
end
disp(zr)

         0   -0.0000    0.0000    3.9266    3.9266    3.9266    7.0686    7.0686    7.0686   10.2102   10.2102   10.2102   13.3518   13.3518   13.3518   13.3518   16.4934   16.4934   16.4934

figure
xx = linspace(0,18,100);
plot(xx,det_a(xx),zr,0,'o')
grid on
ylim([-10 10])
xlabel('\betal')

[Gerry Oscar]

Works for me, thanks!

[Gerry Oscar]

If I may enquire again, how would I go by doing the same thing except trying to find the intersections at different values of y, for example all intersections at y = -2

[Alan Stevens]

Simply add 2 to the end of the det_a function definition.

[Gerry Oscar]

Hmm.. not sure what you mean by that.

[Alan Stevens]

fzero finds the value of x that makes the function det_a equal zero. So if it makes det_a+2 equal zero, then det_a must be -2.

Something like this:

det_a = @(x) sin(x).*cosh(x) - cos(x).*sinh(x);
det_b = @(x) det_a(x) + 2;
x=0:18;
zr = zeros(1,numel(x));
for i = 1:numel(x)
    zr(i) = fzero(det_b, x(i));
end
disp(zr)

   -1.4526   -1.4526    3.9795    3.9795    3.9795    3.9795    7.0662    7.0662    7.0662   10.2103   10.2103   10.2103   13.3518   13.3518   13.3518   13.3518   16.4934   16.4934   16.4934

figure
xx = linspace(0,18,100);
plot(xx,det_a(xx),zr,-2,'o')
grid on
ylim([-10 10])
xlabel('\betal')

[Gerry Oscar]

Riight, thanks!

Answer 2

[KSSV]

You can consider using this: https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections