-t/6, 2 
Bat eat ie e+e 1h | 
oye ie it aie VT we?) ao aa oe 
rs 2 [1+ 2/8, fe Soe Ya Her]? ) 
(4.17) 
4 
(1+ Mo]4,) 
foe oH /2) 7 
) 
r -t/9 
W/O, 5 ee” © ant ie dnitbed 
where properly terms of the order @ 
to be consistent with the peak approximation to Blt) . If we add Eq. 
4,17 to the peak formula for @&) of Eq. 4.10 and suppress such terms, 
the resulting expression for G,( &) \ is slightly in error for be =O. 
Since, however, te/, 2 is small relative to W in the initial stages of the 
motion, a suitable interpolation formula for Gt) » accurate for t=0 
and for long times, and consistent with the peak approximations of Eq. 4.10 
and 4.17 is the following, = 
-t/B, eey re 
G(t) = ¢@, C2), + a, fd, B, 
(4.18) 
Qe ps (l-Alu se, QL o= Au Ck", 
Since 1@ 7 is in gmeral small relative to £2,, » the complete peak approx- 
imation, 
-t/8, 
eat = er ae, 
G = a, (W,+ wi/2) = ro yee ; 
(4.19) 
may be used for small values of t when 56,/4 does not differ greatly 
tron O,. If Eq. 4.19 is employed to represent G(t) , the tail of the 
shock wave will of course be distorted since the exponential differs widely 
ae 
