U=0.1;
k=[0.01:0.01:2];
omvar=(k*U).*(1+i*(tanh(k*h).^(1/2)))./(1+(tanh(k*h)));
omsin=(k*U).*(tanh(k*h)+i*(tanh(k*h).^(1/2)))./(1+(tanh(k*h)));

figure;
plot(k, real(omvar),k,imag(omvar));
legend('omvar_r','omvar_i');


figure;
plot(k(2:end),diff(real(omvar))./diff(k));
hold on;
plot(k(2:end),diff(real(omsin))./diff(k));
legend('vg_{var}','vg_{sin}');


