With a sinusoidal input, the output of a linear system is also sinusoidal, and the ratio of the two signal amplitudes is the amplitude response (the modulus of the complex frequency response). An experiment with sinewaves therefore permits an immediate check of the response, without any a-priori knowledge of its mathematical form and without waveform modelling; this is often the first step in the identification of an unknown system. A computer program would however be required for converting discrete values of the response function into a parametric representation; a calibration with arbitrary signals as described later is more straightforward for this purpose.
When only analog equipment is available, the calibration coil or the shake table may be driven with a sinusoidal test signal and the input and output signals recorded with a chart recorder or an X-Y recorder. On the latter, the signals should be be plotted as a Lissajous ellipse from which both the amplitude ratio and the phase can be read with good accuracy [Mitronovas & Wielandt 1975]. The signal period should be measured with a counter or a stop watch because the frequency scale of sinewave generators is often inaccurate.
The accuracy of the graphic evaluation depends on the purity of the sinewave. A better accuracy can of course be obtained with a numerical analysis of digitally recorded data. By fitting sinewaves to the signals, amplitudes and phases can be extracted for just one precisely known frequency at a time; distortions of the input signal then don't matter. For best results, the frequency should be fitted as well, the fit should be computed for an integer number of cycles, and offsets should be removed from the data. A FORTRAN program "SINFIT" is offered for this purpose (section 11).