MATLAB: Area of a closed curve in a complex plane

areacurve

Hi! Is there a way I can compute the area of the following complex curve:

clear all
close all
clc
c=0.1;
a = c/4;
b = 0.01;
lambda = 0.01;
R = sqrt((a+b)^2+lambda^2);
m = sqrt(b^2+lambda^2);
delta = pi/2+atan(b/lambda);
theta=linspace(0,2*pi,10000);
zeta_c = -b + 1i*lambda + R.*exp(1i*theta);
zeta_w= zeta_c + a^2./zeta_c;
figure,
plot(zeta_w), axis equal, grid on

Thanks!

Best Answer

>> polyarea(real(zeta_w),imag(zeta_w))
ans =
      0.0029
>>

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MATLAB: How to find certain point (ex. maximum y value, or certain y value with respect to certain x value) from a function/plot I made

Use the max function and the interp1 function:

M=300;
K=21000;
C=2000;
A=0.2;
wn=sqrt(K/M);
zeta=C/(2*sqrt(M*K));          % these are all constants
 
syms w
hp = fplot(sqrt(wn^4+(2*zeta*wn*w)^2)/sqrt((wn^2-w^2)^2+(2*zeta*wn*w)^2),[0 100]);
title('|G(jw)| vs w')
xlabel('w (rad/s)')
ylabel('|G(jw)|')
xd = get(hp, 'XData');
yd = get(hp, 'YData');
[maxGjw,idx] = max(yd);
Gjw01 = interp1(yd(idx:end), xd(idx:end), 0.1);
fprintf('Maximum G(j%.2f) = %.2f\nG(j%.2f) = 0.1\n', xd(idx),maxGjw,Gjw01)

to get:

Maximum G(j7.47) = 1.66
G(j68.15) = 0.1

MATLAB: How to plot all the data point in a for loop

No loop needed:

w = 1:100 ; 
lambda = 1./w;
g1 = (w.^2.*lambda.^2)./(1+w.^2.*lambda.^2);
g2 = (w.*lambda.^2)./(1+w.^2.*lambda.^2);
plot(w, g1, w, g2)

If you want a loop (which is not required)

w = 1:100 ; 
g1 = zeros(size(w)) ; 
g2 = zeros(size(w)) ; 
for i=1:100
    lambda = 1/w(i) ;
    g1(i) = (w(i)^2*lambda^2)/(1+w(i)^2*lambda^2);
    g2(i) = (w(i)*lambda^2)/(1+w(i)^2*lambda^2);
end
plot(w, g1, w, g2)

Best Answer

Related Solutions

MATLAB: How to find certain point (ex. maximum y value, or certain y value with respect to certain x value) from a function/plot I made

MATLAB: How to plot all the data point in a for loop

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