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

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Gerry Oscar
Gerry Oscar on 20 Oct 2021
Commented: Gerry Oscar on 21 Oct 2021
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!

Accepted Answer

Alan Stevens
Alan Stevens on 20 Oct 2021
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')
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