% Plots for damped oscillators
clear all
hf=figure('PaperUnits','inches','PaperSize',[5 5]);
set(hf,'PaperPosition',[0 0 5 5]);
%
t=linspace(0,10);
om0=2*pi/2.5;
A=10;
%
gam1=om0/4;
om1=sqrt(om0^2-(gam1/2)^2);
env=A*exp(-gam1*t/2);
xu=env.*cos(om1*t);
%
gam2=3*om0;
alph1=(gam2/2)*(1+sqrt(1-4*om0^2/gam2^2));
alph2=(gam2/2)*(1-sqrt(1-4*om0^2/gam2^2));
C1=A*(gam1/2-alph2)/(alph1-alph2);
C2=A-C1;
xo=C1*exp(-alph1*t)+C2*exp(-alph2*t);
%
gam3=2*om0;
alph=gam3/2;
D1=A;
D2=(alph-gam1/2)*A;
xc=D1*exp(-alph*t)+D2*t.*exp(-alph*t);
%
h=plot(t,zeros(size(t)),'k',t,xu,'r',t,env,'--r',t,xo,'b',t,xc,'g');
set(h,'Linewidth',2)
%
set(gca,'FontSize',15)
xlabel('Time t','FontSize',20)
ylabel('x(t)','FontSize',20)
%
print -dpdf DHOs.pdf
close(hf)