The time scales and efficiency of plasma heating by resonant absorption of Alfven waves are studied in the framework of linearized compressible and resistive magnetohydrodynamics. The configuration considered consists of a straight cylindrical axisymmetric plasma column surrounded by a vaccum region and a perfectly conducting shell. The plasma is excited periodically by an external source, located in the vacuum region. The temporal evolution of this driven system is simulated numerically. It is shown that the so-called 'ideal quasi-modes' (or 'collective modes') play a fundamental role in resonant absorption, and affect both the temporal evolution of the driven system and the efficiency of this heating mechanism considerably. The variation of the energetics in periodically driven resistive systems is analysed in detail for three different choices of the driving frequency, viz an arbitrary continuum frequency, the frequency of an ideal 'quasi-mode', and a discrete Alfven wave frequency. The consequences for Alfven' wave heating of both laboratory plasmas and solar coronal loops are discussed.