  The damped oscillating structures recently revealed by a three parametric
formula from the proton ``effective'' form factor data extracted of the
measured total cross section $\sigma^{bare}_{tot}(e^+e^-\to p\bar p)$ still
seem to have an unknown origin. The conjectures of their direct manifestation
of the quark-gluon structure of the proton indicate that they are not specific
only of the proton and neutron, but they have to be one's own, similar to other
hadrons.
  Therefore, the oscillatory structures from the charged pion electromagnetic
form factor timelike data, extracted of the process $e^+e^-\to \pi^+ \pi^-$ are
investigated by using the same procedure as in the case of the proton.
  The analysis shows the appearance of the oscillating structures in the
description of the charged pion electromagnetic form factor timelike data by
three parametric formula with a rather large value of $\chi^2/ndf$, while the
description of the data by the physically well-founded Unitary and Analytic
model has not revealed any damped oscillating structures.
  From the obtained result on the most simple object of strong interactions,
one can conclude that damped oscillating structures received from the
``effective'' proton form factor data are probably generated by a utilization
of the improper three parametric formula which does not describe these data
with sufficient precision.
