i need some help with finding the damping ratio

i need to find the damping ratio of the graph (attached 238). the function to do this is given (attached 236)

i am unsure how to do this i have the x and y coordinates for each of the points in the graph

X0 = (0,2)

x1= (12.73,0.77)

x2= (25.36,0.29)

x3=(37.99,0.11)

what would the codebe to find zeta?

Answer 1

[Alan Stevens]

Use fzero:

x = [12.73, 25.36, 37.99];
y = [0.77, 0.29, 0.11]/2;

zeta = fzero(@(zeta) fn(zeta,y),0.5);

disp(['zeta = ' num2str(zeta)])

zeta = 0.1517

disp('Compare values:')

Compare values:

for n = 1:3
   disp([y(n), exp(-2*pi*n*zeta/(sqrt(1-zeta^2)))]) 
end

    0.3850    0.3812

    0.1450    0.1453

    0.0550    0.0554

function Z = fn(zeta,y)
         Z = 0;
         for n = 1:3
           Z  = Z + log(y(n))-(-2*pi*n*zeta/(sqrt(1-zeta^2)));
         end
        
end