In recent years many methods have been proposed for the measurement of the frequency response of linear systems but the method most often used in the study of structures is the steady state vector response method, the natural frequencies and damping ratios being measured from the resulting vector diagrams. This method is tedious and time consuming and often cannot be readily applied outside the laboratory. Some effort has been directed in the past to employ quasi-steady state methods such as the slow frequency sweep technique but errors are introduced because the response at resonance is less than the steady state maximum and the frequency at which the maximum occurs is shifted in the direction in which the excitation frequency is changing. Additional errors are introduced in the analysis of the system response because of the necessary averaging time of the function analyser used to derive the vector diagrams. Some refinements in technique have been proposed by Reed who developed the “λ Law” frequency sweep in which the percentage change in frequency per cycle is constant. This offers some reduction in test time when compared with logarithmic and linear frequency sweeps but a knowledge of the minimum damping likely to be encountered at any resonant frequency within the sweep range is essential so that the method may be employed advantageously.