How do you graph ω² in a Bode Plot?
You just calculate it and plot it:

In Matlab:  

&gt;&gt; w=logspace( -1 , 10,10000);
&gt;&gt; xfun = .1*w.^2.*(1 - (w./10).^2 +j*w./2)./((1+j.*w).*(1+j.*w/100).^3);
&gt;&gt; subplot(2,1,1)
&gt;&gt; semilogx(w, 20*log10(abs(xfun)))
&gt;&gt; subplot(2,1,2)
&gt;&gt; semilogx(w, angle(xfun)*180/pi)][1]][1]




You could just use "bode", but that's easier w/ the Laplace transform.  Because I didn't, the x-axes are in radians, with no labels.  I adjusted the line widths and font sizes for export to a jpg.

If you don't have Matlab, this should work directly in Octave, which is free.  If the freq scale is off, feel free to adjust w.  If you want freq in Hz, remember that \$\omega=2\pi f\$

As a tip, remember that your exponents need to be ".^", not "^", and your multiplies and divides need to be ".*" and "./" -- all for element-by-element operations.

If you're just interested in \$\omega^2\$, \$20log_{10}\omega^2 = 40log_{10}\omega\$.  At \$\omega=0.1\$, this is equal to -40dB, and it will have a slope of 40db/decade.  Perhaps even more intuitively, it is 0dB at \$\omega=1\$.  It is real, so the angle is 0.

&gt;&gt; w=logspace( -1 , 10,10000);
&gt;&gt; w2=w.^2;
&gt;&gt; subplot(2,1,1)
&gt;&gt; semilogx(w, 20*log10(abs(w2)))
&gt;&gt; subplot(2,1,2)
&gt;&gt; semilogx(w, angle(w2))




This, of course gives you 80dB/decade total going up, above 100 rad/sec, and 80 going down, for a flat line.