928 
BFet | ded o/s i sit’ wt 
In =| F +E VL - Fll - cos wt,) - —————2 __. (1-45) 
4V1l- 21 - cos at,) 
Wall 
If the gauge is oriented against 
the rigid surface as shown in Fig. I-8, 
t,. ts approximately 25 microsece ‘Then 
Gauge 
eee 
at, = 0-505 for 5/32 in. balls Direction of 
(1-46) travel of wave 
at, = 0.455 for $/8 in. balls. 
Pig. I-8. 
Putting Eq. (I-46) into Eq (I-45), 
Xn = 0-971 = for 5/32 in. balls 
BF 
In = 0.936 ET for 3/8 in. balls. 
10- Initial Deformation 
Apply a step pressure wave F H(t) to a gauge in which the piston starts 
from rest in contact with a ball having initial deformation 
Xo° 
The boundary conditions are given by x = X and x=0 at t = 0, and the 
equation of motion becomes: 
2 
x H(t 
x=—+— apr hp ae ee (I-47) 
D,” +o Ml D, +@ 
x =< (1 = cos wt) H(t) + Ip cos wt H(t) (I-48) 
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