
Historically swept sine tests normally define, over a frequency range a, constant peak displacement or constant peak velocity or constant peak acceleration.
This was simply because the method to control this was easier as it was only a case of integration or double integration, and for analogue controllers this was straight forward.
Thus the situation was as follows:
If displacement was kept a constant value over a frequency range the slope would be based on the fact that the acceleration would increase by a factor of 4 for every octave (frequency has doubled)
This would mean that the slope would be an increase of approximately 12.0411998265593dB per octave : Actually to be more precise 40dB per decade.
However, if velocity was kept a constant value over a frequency range the slope would be based on the fact that acceleration would increase by a factor of 2 for every octave (frequency has doubled)
This would mean that the slope would be an increase of approximately 6.0205999132796dB per octave : Actually to be more precise 20dB per decade.
Modern controllers which are digital can accept slopes which do not have to comply with the above.
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