  We develop a theory for polymer translocation driven by a time-dependent
force through an oscillating nanopore. To this end, we extend the iso-flux
tension propagation theory (IFTP) [Sarabadani \textit{et al., J. Chem. Phys.},
2014, \textbf{141}, 214907] for such a setup. We assume that the external
driving force in the pore has a component oscillating in time, and the
flickering pore is similarly described by an oscillating term in the pore
friction. In addition to numerically solving the model, we derive analytical
approximations that are in good agreement with the numerical simulations. Our
results show that by controlling either the force or pore oscillations, the
translocation process can be either sped up or slowed down depending on the
frequency of the oscillations and the characteristic time scale of the process.
We also show that while in the low and high frequency limits the translocation
time $\tau$ follows the established scaling relation with respect to chain
length $N_0$, in the intermediate frequency regime small periodic fluctuations
can have drastic effects on the dynamical scaling. The results can be easily
generalized for non-periodic oscillations and elucidate the role of time
dependent forces and pore oscillations in driven polymer translocation.
