1. Import the file ExperimentalData2.txt to your MATLAB folder. (I have the data so just ignore this step)

The experimental data is two columns of numbers (for example: (first row) -1.51058, 0.230909).

2. Fit the experimental data to the function

(1)

with fitting parameters I₀, w, q and . Can you guess the value for I₀ and ? Hint: Evaluate Eq. (1) at x = 0. Use your guessed values for I₀ and as initial parameters. For w and q use 1 and 10, respectively.

3. Plot the experimental data and the fitted line in the same plot. Add position (mm) and intensity (a.u.) as your x and y axis labels. Do not forget a legend for your plot. (Just write the code on matlab as if you had the data, no need to run it to show me the graph because it wont work (as you probably know))

4. Does your fitted line look uneven? Try to plot your fitted line using more points to your independent variable. Hint: Define a new column vector with elements from -1.5 to 1.5 in steps of 0.01 and use it into the command predict. (Again just write the code)

5. The experimental data seems to have a Gaussian envelope. Plot that envelope in the same plot and report its full width at half maximum (FWHM). Add the corresponding label on the plot legend. Hint 1: What happens if you simply ignore the cosine function in Eq. (1) and plot the resulting expression? Hint 2: A general Gaussian function centered at x = 0 is given by

(2)

Where is the standard deviation. The FWHM for this Gaussian function is (Same here)

Thank you for the help