In class we made an approximation when we derived the complex Lorentzian line sh

Question

In class we made an approximation when we derived the complex Lorentzian line shape for the motion of a forced damped oscillator. If the driving frequency is close to the resonant frequency (omega omega0), then: 1/omega20 - omega2 - j omega gamma = 1/(omega0 - omega)(omega0 + omega) j omega gamma 1/2 omega 0( omega 0 - omega )-jomega0gamma In this problem, we will explore the validity of this approximation. Let's use some typical numbers: for water vapor, a strong absorption line is found in the terahertz region of the spectrum, at upsilon0 = 557 GHz. The line width of this resonance is given by gamma = 2pi times (200 MHz). Using Matlab, make plots of the both the exact and approximate forms given above on the same graph (you will only be able to tell the difference if you use a log scale). Make a separate plot for the real and imaginary parts of the two expressions. Comment on these graphs.

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MATLAB (matrix laboratory) is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran. Although MATLAB is intended primarily for numerical computing, an optional toolbox uses the MuPAD symbolic engine, allowing access to symbolic computing capabilities. An additional package, Simulink, adds graphical multi-domain simulation and Model-Based Design for dynamic and embedded systems. In 2004, MATLAB had around one million users across industry and academia.[2] MATLAB users come from various backgrounds of engineering, science, and economics. MATLAB is widely used in academic and research institutions as well as industrial enterprises.

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