Plotting Systems in Matlab: x_1(t),x_2(t) w/ Complex Equations

[Tom McCurdy]

How would you plot

$$x_1(t)=c_1e^{-t}+c_2*e^{3t}$$
$$x_2(t)=-c_1e^{-t}+c_2*e^{3t}$$

and similar systems in Matlab?

For example if it was complex like:

$$x_1(t)=5*e^{5t}(c_1 cos(4t)+c_2sin(4t))$$
$$x_2(t)=5*e^{5t}((2 c_1+4 c_2) cos(4t)+(4 c_1 - 2 c_2)sin(4t))$$

 

[ziad1985]

in MATLAB type:
help plot

 

[tacman]

To plot these systems in Matlab, you would first define the time variable t as a vector with the desired range. Then, you can use the "plot" function to plot each equation separately, specifying the time variable as the x-axis and the equation as the y-axis. For the first set of equations, the code would look like this:

% Define time variable
t = linspace(0,10); % change the range as needed

% Define constants
c1 = 2;
c2 = 3;

% Plot x1(t)
x1 = c1*exp(-t) + c2*exp(3*t);
plot(t,x1)

% Plot x2(t)
x2 = -c1*exp(-t) + c2*exp(3*t);
plot(t,x2)

For the second set of equations, the code would be similar, but you would need to use the "cos" and "sin" functions to incorporate the complex component. The code would look like this:

% Define time variable
t = linspace(0,10); % change the range as needed

% Define constants
c1 = 5;
c2 = 2;

% Plot x1(t)
x1 = c1*exp(5*t)*(c1*cos(4*t) + c2*sin(4*t));
plot(t,x1)

% Plot x2(t)
x2 = c1*exp(5*t)*((2*c1 + 4*c2)*cos(4*t) + (4*c1 - 2*c2)*sin(4*t));
plot(t,x2)

You can also add labels, titles, and legends to your plot to make it more clear and organized. Overall, the key is to define the time variable, use the appropriate functions to incorporate the complex component, and then plot each equation separately.