Having issues plotting with imaginary values. Need help checking results.

 The question I am trying to complete is stated in the given image. This is what I have so far but I'm thinking it is incorrect and could use some help debugging. I need to plot H vs Omega

clc
  clear all
  fr=linspace(0,4,100);
  dr1 = 0;
  dr2 = 0.1;
  dr3 = 0.2;
  dr4 = 0.4;
  dr5 = 0.5;

    H1=1./((1-fr.^2)+(2*dr1*fr).^2).^(0.5)
    omega1 = (180/pi)*atan((2*dr1*fr)./(1-fr.^2))
    plot(imag(H1),omega1)

    hold on

    H2=1./((1-fr.^2)+(2*dr2*fr).^2).^(0.5)
    omega2 = (180/pi)*atan((2*dr2*fr)./(1-fr.^2))
    plot(imag(H2),omega2)

    H3=1./((1-fr.^2)+(2*dr3*fr).^2).^(0.5)
    omega3 = (180/pi)*atan((2*dr3*fr)./(1-fr.^2))
    plot(imag(H3),omega3)

    H4=1./((1-fr.^2)+(2*dr4*fr).^2).^(0.5)
    omega4 = (180/pi)*atan((2*dr4*fr)./(1-fr.^2))
    plot(imag(H4),omega4)

    H5=1./((1-fr.^2)+(2*dr5*fr).^2).^(0.5)
    omega5 = (180/pi)*atan((2*dr5*fr)./(1-fr.^2))
    plot(imag(H5),omega5)

Answer 1

[KSSV]

N = 100 ;
fr=linspace(0,4,N);
dr = [0; 0.1; 0.2; 0.4; 0.5];
H = zeros(length(dr),N) ;
omega = zeros(length(dr),N) ;
for i = 1:length(dr)
    H(i,:)=1./((1-fr.^2)+(2*dr(i)*fr).^2).^(0.5) ;
    omega(i,:) = (180/pi)*atan((2*dr(i)*fr)./(1-fr.^2)) ;
end
figure ;loglog(fr,abs(H),'r') ;
figure ; plot(fr,omega,'b') ;

Go through the text book of the concepts once, find out what to plot w.r.t what. I did it long ago and unable to recollect.