How to find second order transfer function from a graph?
Here is a "quickie" way of capturing \$ \omega \$ by eye. Measure the time for one cycle. Use the zero-crossing points, translated by the steady-state (+2.5 in this case) to give you a time \$t\$.
 This time measurement gives you frequency \$f= 1/t\$.
Then \$ \omega = 2\pi f\$:

You can use any of the many cycles along the steady state line to measure \$t\$; they should all have the same period. The first cycle will be the largest, where you can see its steady-state crossing points easiest. Cycles following the first have less amplitude, so that estimating where they cross steady-state becomes more difficult.
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When waveforms are quickly damped, this method is difficult to apply...it is appropriate for slowly-damped waveforms. Some folks measure time from one peak to the next. This is less accurate with a quickly-damped waveform.