l-conformal Newton-Hooke symmetry of the damped Pais-Uhlenbeck oscillator

Two Lagrangian formulations for describing the damped harmonic oscillator have been introduced by Bateman. For these models we construct higher derivative generalizations which enjoy the l-conformal Newton-Hooke symmetry. It is shown that the dynamics of generalized systems corresponds to the damped Pais-Uhlenbeck oscillator for a particular choice of its frequencies.