The development of a mechanical, damped, forced, harmonic oscillator system with computer data acquisition and analysis was undertaken. The original aim was to make accurate comparisons of experimental data with the standard textbook analyses, especially with regard to the phase difference between the displacement response and the driving force, and to the functional form of the displacement response versus frequency curve. Accurate measurements of the phase and amplitude for the displacement responses for the system developed indicated that for real systems with damping, the conventional analysis needs to be revised. If electromagnetic damping is used, the effective restoring forces must include the electromagnetic forces resulting from the interaction of the ‘‘eddy’’ currents with the damping magnetic field, and this can be considered as increasing the effective spring constant. When viscous damping is used, fluid adhering to the damping system changes the effective oscillating mass. Both of these effects will change the resonant frequency. Experimental data and analysis are presented to confirm the revised theoretical treatment.