Problem L$8\mathrm{.}2$ Approximations. When drawing straight line Bode plots we've been approximating the following system when $<mn>1</mn>$ :

$\frac{1}{s^2+2{}_{n}s+{}_n^2}$~~$\frac{1}{s^2+{}_n^2}$

For:

$($a$)$ Draw a straight line approximation using MATLAB with $w_n$ of your choice $($include your handwritten calculations: DC gain, cutoff frequency,... and use MATLAB instead of manually drawing$).$

$($b$)$ For several values of $<mn>1</mn>$ compare your straight line approximation from $($a$)$ to an exact Bode plots using the same figure. How do they compare?

$($c$)$ Add an exact Bode for $=1.$

$($d$)$ Add an exact Bode for $>1.$

What can you conclude from your analysis? You can use bode or manual MATLAB code to plot the diagrams. PLEASE PROVIDE MATLAB CODE FOR ALL PARTS