*(Page 5)*

*Peak Acceleration*of a random test, we will find the

**(g**area under the Power Spectral Density curve, take its square root and multiply it by 3. The required

_{rms)}^{2}*Peak Velocity*and

*Peak Displacement*terms can be found by synthetically integrating and double integrating the Acceleration PSD (dividing the amplitude of that spectrum by

**ω=2πf**and by

**w**) and repeating these actions.

^{2}At first glance, it would appear that calculating the area beneath the random test’s PSD would be a simple matter. Most test specifications contain a profile composed of straight-line segments, so that the required area is made up of triangles, rectangles and trapezoid – shapes with simple area formulas. But those spectra present the

**g**versus frequency on a^{2}/Hz*log/log*plot such as Figure 12. When the same spectrum is presented as a linear/linear graph (such as Figure 13), it becomes obvious that the inclined “lines” are actually curves.In order to find the area under each (**log** **A** versus **log** **f**) PDF segment, we will need to have the **A(f)** equation for each curve. On the log/log plot, each straight-line segment can be described by:

*y = mx + b*

Where:

y = log_{10}(A)

x = log_{10}(f)

m = log_{10}(A_{2}) - log_{10}(A_{1}) / log_{10}(f_{2}) - log_{10}(f_{1}) = log_{10}(A_{2}/A_{1}) / log_{10}(f_{2}/f_{1})

b = log_10(A_1 )

Hence:
log_{10}(A) = mlog_{10}(f) + log_{10}(A_{1})

From which:

1) A = A_{1}f^{m} (g^{2}/Hz)