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"The APSD must be approximately uniform over the half power bandwidth of each oscillator." 1

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You have to have in mind the plot of the FRF of an oscillator. There are three areas : spring, damper and mass.
The damper area is the most energetic and the most "narrow band".
So suppose you excite the oscillator in the whole frequency range (white noise) in a first time, next you excite the oscillator with a white noise filtered in the damper area, i.e. in the half power bandwith in a second time.

In the both cases, the vibration energy is quite the same.
So you can neglect spring and mass effects as indicated by eq. 15.

If you don't respect this assumption, then you can't writte the eq. 15.
 
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