  The transition of an impulsively excited kink oscillation of a solar coronal
loop to an oscillation with a stationary amplitude, i.e., the damping pattern,
is determined using the low-dimensional self-oscillation model. In the model,
the decayless kink oscillations are sustained by the interaction of the
oscillating loop with an external quasi-steady flow. The analytical solution is
based on the assumption that the combined effect of the effective dissipation,
for example, by resonant absorption, and interaction with an external flow, is
weak. The effect is characterised by a dimensionless coupling parameter. The
damping pattern is found to depend upon the initial amplitude and the coupling
parameter. The approximate expression shows a good agreement with a numerical
solution of the self-oscillation equation. The plausibility of the established
damping pattern is demonstrated by an observational example. Notably, the
damping pattern is not exponential, and the characteristic decay time is
different from the time determined by the traditionally used exponential
damping fit. Implications of this finding for seismology of the solar coronal
plasmas are discussed. In particular, it is suggested that a very rapid, in
less than the oscillation period, decay of the oscillation to the stationary
level, achieved for larger values of the coupling parameter, can explain the
relative rareness of the kink oscillation events.
