JE() equals A at 2n/T. 
Example two is a slight extension of the concepts in 
example ones E(p) has three steps. ~() can be arbitrary 
except in the intervals surrounding the points or/T § 20/T55 
and an/T where it is given by equation (7.15). The value of 
the integral is given by equation (7.17) and P.E. is given by 
equation (7.18). The graphs of the approvriate functions are 
given in figure 13. 
Example three is the formulation of the Power Intesral for 
the infinite train of regular wave groups defined by equation 
(6.8). E(u), as defined by eouaeien (7.19), is a step function 
with an infinite number of steps which become small like 
exp[-p 7] aS # approaches infinity. E aig therefore exists. 
n 
Y(#) can be defined by equation (7.20) as one of many possible 
ways. The integral and the average potential energy are then 
given by equations (7.21) and (7.22). The various functions 
involved are graphed in figure 13. , 
Example four shows how it is possible to pick E(#) and 
VCR) in a way which will yield physically unrealistic results 
for 7(t). If E(H) is continuous and, for example, a linearly 
increasing function of # over part of the #! axis as given by 
equation (7.23), and if W(H) is zero, the limit, as the mesh 
approaches zero in equation (7.7), becomes infinite at t = 0. 
Let the net points be equally spaced at intervals of AP such 
that mAp = 2r/T,. Then at t = 0, the cosine term is unity 
and the value of (0) is given by equation (7.25). As m ap- 
proaches infinity, and Aw approaches zero, 7) (0) becomes 
= 132 - 
