%PLOT k_r VERSUS R
M=E1(1)
w=E2(1)
R=3:.001:7;  
%only when c0=1, otherwise add c0 term
aKr=sqrt(  (w+G*M./(2*pi*R.^2)).^2 - M^2./R.^2 );
figure(5);
plot(R,real(aKr));
title('Figure 5:  |\itk_r\rm| versus \itr\rm for path in Figure 4');
xlabel('radius')
ylabel('|\itk_r\rm|')
hold on
plot(R,imag(aKr),':')
axis([3 7 -.2 1.5])
legend('Real        part of |\itk_r\rm|','Imaginary part of |\itk_r\rm|',0)
hold off