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In this paper we study a two-dimensional [2D] rotationally symmetric harmonicoscillator with time-dependent frictional force. At the classical level, wesolve the equations of motion for a particular case of the time-dependentcoefficient of friction. At the quantum level, we use the Lewis-Riesenfeldprocedure of invariants to construct exact solutions for the correspondingtime-dependent Schr\"{o}dinger equations. The eigenfunctions obtained are interms of the generalized Laguerre polynomials. By mean of the solutions weverify a generalization version of the Heisenberg's uncertainty relation andderive the generators of the $su(1,1)$ Lie algebra. Based on these generators,we construct the coherent states $\grave{\textrm{a}}$ la Barut-Girardello and$\grave{\textrm{a}}$ la Perelomov and respectively study their properties.

Lewis-Riesenfeld quantization and SU(1,1) coherent states for 2D damped harmonic oscillator