% plot function y as sum of two aperiodic modes (real exponential functions)  
% y= exp(-t)+4*exp(-4t)
% 

clear all
close all
clc

% define exp coefs.
lambda_1=-1;
lambda_2=-4;

% define the corresponding time constants
tau_1=-1/lambda_1;
tau_2=-1/lambda_2;

% define time vector (final time, t_f, and, sampling time, t_s)
if tau_1>=tau_2
    t_f=5*tau_1;
    t_s=tau_2/10;
else
    t_f=5*tau_2;
    t_s=tau_1/10;
end

% time vector
time=0: t_s:t_f; % or time=0:0.01:5
% define y1
y1=exp(lambda_1*time);
% define y2
y2=4*exp(lambda_2*time);

%define y
y=y1+y2;

% plot y, y1 and y2
figure(1)
plot(time,y1,'-b');
hold on
grid on
plot(time,y2,'-r');
plot(time,y,'-g','LineWidth',3)
legend('y_1','y_2','y')
xlabel('time')