  We consider single particle and polymer translocation where the frictional
properties experienced from the environment are changing in time. This work is
motivated by the interesting frequency responsive behaviour observed when a
polymer is passing through a pore with an oscillating width. In order to
explain this better we construct general diffusive and non-diffusive frequency
response of the gain in translocation time for a single particle in changing
environments and look at some specific variations. For two state confinement,
where the particle either has constant drift velocity or is stationary, we find
exact expressions for both the diffusive and non-diffusive gain. We then apply
this approach to polymer translocation under constant forcing through a pore
with a sinusoidally varying width. We find good agreement for small polymers at
low frequency oscillation with deviations occurring at longer lengths and
higher frequencies. Unlike periodic forcing of a single particle at constant
mobility, constant forcing with time dependent mobility is amenable to exact
solution through manipulation of the Fokker-Planck equation.
