First set α = 𝛽 = 0 and check that the frequency doesn’t depend on amplitude.
Next, set α = 0, 𝛽 = 1 and try amplitudes (initial x, taking initial v = 0) 0.1, 0.5, 1, for example, see how
the frequency changes. Can you give a qualitative explanation?
Next, set 𝛽 = 0 and take gradually increasing values of α.
At some point, things will go bad. Why?
Explore possibilities with both α,𝛽 nonzero.
Here's the relevant lecture.
Program by: Carter Hedinger