  We study the energy deposition in a one dimensional interacting quantum
system with a point like potential modulated in amplitude. The point like
potential at position $x=0$ has a constant part and a small oscillation in time
with a frequency $\omega$. We use bosonization, renormalization group and
linear response theory to calculate the corresponding energy deposition. It
exhibits a power law behavior as a function of the frequency that reflects the
Tomonaga-Luttinger liquid (TLL) nature of the system. Depending on the
interactions in the system, characterized by the TLL parameter $K$ of the
system, a crossover between week and strong coupling for the backscattering due
to the potential is possible. We compute the frequency scale $\omega_\ast$, at
which such crossover exists. We find that the energy deposition due to the
backscattering shows different exponent for $K>1$ and $K<1$. We discuss
possible experimental consequences, in the context of cold atomic gases, of our
theoretical results.
