The study of driven mechanical harmonic oscillations in the undergraduate student laboratory is greatly enhanced by the new high standard of precision achieved by computerized data acquisition and analysis. In this paper, two experiments are described that investigate transient behavior. In one experiment, beats are observed when the driving frequency is not equal to the resonant frequency; and in the other experiment, oscillations are observed to grow linearly with time at the resonant frequency. Steady‐state behavior is also investigated. Both amplitude and phase are measured as functions of frequency.