Linear System
% The amount of charge going through the Resistor1 is directly proportional
% to time
t = [0:0.01:15];
R1 = 1000; % Ohms
V = 50; % Volts
I = V/R1;
Q = I * t;
plot(t,Q)
title('Original')
figure
%When the switch is closed at t=2
Q = I * (t-2);
%Or Equavalently,
t = [2:0.01:17];
Q = I * t;
plot(t,Q)
title('Time Shifted by 2 sec')
File:Circuit.jpg ECE301Fall2008mboutin File:PartC-1.jpg ECE301Fall2008mboutin
Non-Linear System
% Position of a falling object from a 200 m high cliff.
t = [0:0.01:6.8];
y = 200 - 1/2*9.8.*t.^2;
plot(t,y);
xlabel('Time(sec)')
ylabel('Position from the Cliff(m)')
File:Cliff.jpg ECE301Fall2008mboutin In this case, there exist positive time and negative time that would satisfy y = x(t). Thus, this relationship is non-linear.
