*(Page 6)*

**A**is of dimension

**g**where

^{2}/Hz**g**is understood to be an RMS measurement. We require a velocity power spectrum,

**V**, of

**IPS**amplitude and a displacement power spectrum,

^{2}/Hz**D**, of

**inch**dimension where both

^{2}/Hz**IPS**and

**inch**are understood to be RMS units. The required segment equations are:

**f**, over the interval from

**f**to

_{1}**f**. This results in the mean-square values:

_{2}Adding the mean-square for all segments in the PSD yields the total mean-square values of acceleration, velocity and displacement. Taking the square root of each mean-square provides the RMS value. Multiplying the RMS values for **g ^{2}**,

**IPS**and

^{2}**inch**by 3 provides the peak acceleration, velocity and displacement. Multiply the displacement result by 2 to obtain a peak-to-peak value. Let’s consider an example.

^{2}Note that some specifications will specify the slope of rising or falling segments. The slope is normally presented in either *dB/octave* (decibels per frequency doubling) or *dB/decade* (dB change over a ten-to-one frequency span). This allows m to be evaluated as:

**f**, and

**g**of the four points defining this three-segment spectrum were placed in an Excel® spreadsheet. The mean-square values of

^{2}/Hz**g**,

^{2}**IPS**and

^{2}**inch**for each segment were computed using equations 4, 5 and 6. The results for all segments were summed and the required conversion to peak and peak-to-peak values made. These calculations are summarized in Figure 15.

^{2}