Variable equations with Euler

I have to write an equation that includes e^(w1*t). Here, w1 is a previously defined single value (such as 2), and "t" is an unknown variable. The intent is to define the equation with all variables having values except "t", and then plotting the results of that equation. How do I go about doing this?

Answer 1

[Umar]

Hi @Zachary,

To achieve the desired outcome in MATLAB, follow a systematic approach. Based on your comments, it is defining the constant ( w1 ), creating a range of values for the variable ( t ), computing the corresponding values of the equation, and finally plotting the results. Below is a step-by-step guide along with the necessary code snippets.

Step 1: Define the Constant

First, define the constant ( w1 ). In this case, set ( w1 = 2 ).

w1 = 2; % Define the constant w1

Step 2: Define the Variable ( t )

Next, create a range of values for the variable ( t ). This can be done using the linspace function, which generates linearly spaced vectors. For example, we can define ( t ) to range from 0 to 5.

t = linspace(0, 5, 100); % Create a vector of 100 points from 0 to 5

Step 3: Define the Equation

Now, define the equation ( y = e^{(w1 * t)} ). In MATLAB, the exponential function is represented by exp(). For more information on this function, please refer to

https://www.mathworks.com/help/matlab/ref/double.exp.html

   y = exp(w1 * t); % Calculate the values of the equation

Step 4: Plot the Results

Finally, plot the results using the plot function, add labels and a title to make the plot more informative.

figure; % Create a new figure window
plot(t, y, 'b-', 'LineWidth', 2); % Plot y against t with blue line
xlabel('Time (t)'); % Label for the x-axis
ylabel('e^{(w1 * t)}'); % Label for the y-axis
title('Plot of e^{(w1 * t)} where w1 = 2'); % Title of the plot
grid on; % Add a grid for better readability

Please see attached.

Hope this helps.

If you have any further questions or need additional assistance with MATLAB functionalities, feel free to ask!