% CASE 1: UNDAMPED

[t,x] = ode45('dyn200',[0 10],[1;1;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 1: Undamped System, Initial Condition = [1;1;0;0]')
pause;

[t,x] = ode45('dyn200',[0 10],[-1;1;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 1: Undamped System, Initial Condition = [-1;1;0;0]')
pause;

[t,x] = ode45('dyn200',[0 10],[1;0;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 1: Undamped System, Initial Condition = [1;0;0;0]')
pause;


% CASE 2: PROPORTIONALLY DAMPED

[t,x] = ode45('dyn210',[0 10],[1;1;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 2: Proportionally Damped System, Initial Condition = [1;1;0;0]');
pause;

[t,x] = ode45('dyn210',[0 10],[-1;1;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 2: Proportionally Damped System, Initial Condition = [-1;1;0;0]');
pause;


[t,x] = ode45('dyn210',[0 10],[1;0;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 2: Proportionally Damped System, Initial Condition = [1;0;0;0]');
pause;

% CASE 3: PROPORTIONALLY DAMPED

[t,x] = ode45('dyn220',[0 10],[1;1;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 3: Proportionally Damped System, Initial Condition = [1;1;0;0]');
pause;

[t,x] = ode45('dyn220',[0 10],[-1;1;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 3: Proportionally Damped System, Initial Condition = [-1;1;0;0]');
pause;

[t,x] = ode45('dyn220',[0 10],[1;0;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 3: Proportionally Damped System, Initial Condition = [1;0;0;0]');
pause;


% CASE 4: NON PROPORTIONALLY DAMPED

[t,x] = ode45('dyn230',[0 10],[1;1;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 4: NON-Proportionally Damped System, Initial Condition = [1;1;0;0]');
pause;

[t,x] = ode45('dyn230',[0 10],[-1;1;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 4: NON-Proportionally Damped System, Initial Condition = [-1;1;0;0]');
pause;

[t,x] = ode45('dyn230',[0 10],[1;0;0;0]); 
twoplot(t,x);
subplot 211
title('CASE 4: Proportionally Damped System, Initial Condition = [1;0;0;0]');
pause;