On equating equations (a) and (c), we get
Equation (e) gives the magnitude of the unbalance and equation (h) gives the magnitude of the phase angle, the direction or sense of the phase cannot be obtained from only three measurements, a fourth measurement by keeping the unit unbalance at 900 (or at 2700) will be required. Let us take a3 be the fourth measurement, now obtain the condition by which the direction angular position,θ, of the unbalance, x, can be obtained. This is left to the reader as an exercise.
Answer
Figure 13.15 Geometrical constructions of unbalance vectors
The difference in the values of unbalance and angular position is due to rounding off error and the error due to the graphical construction.