amplitudes of both high harmonics An−1 /A1 and An+1 /A1 , given by equation (14),
at n ภ 1 are almost equal and approach to the common value 1/(√2n) = mmin /2, in
accordance with equation (7) that describes the n-period subharmonic oscillations as
a superposition of the slow and rapid motions.
With gravity, these complex n-periodic “multiple-nodding” modes exist both for the inverted and non-inverted pendulum.