  We study the response of one-dimensional liquid $^4$He to weak perturbations
relying on the dynamical structure factor, $S(q,\omega)$, recently obtained via
ab-initio techniques [Phys. Rev. Lett. 116, 135302 (2016)]. We evaluate the
drag force, $F_v$, experienced by an impurity moving along the system with
velocity $v$ and the static response function, $\chi(q)$, describing the
density modulations induced by a periodic perturbation with wave vector $q$.
