i need some help with finding the damping ratio

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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?

Answers (1)

Alan Stevens
Alan Stevens on 6 Mar 2022
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

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