907 
RESPONSE OF THE BALL CRUSHER GAUGE TO VARIOUS DRIVING FUNCTIONS 
by 
A. B. Arons 
Woods Hole Oceanographic Institution 
le Introduction 
The fundamental principles and theory of the ball crusher type gauge 
have been thoroughly discussed by several authorse It is the purpose of this 
appendix to present certain useful numerical results concerning the response 
of the ball crusher gauge to various types of driving functions which idealize 
conditions likely to occur in explosives work. 
2. The Fundamental Equation of Motion 
The equation of motion of the ball crusher gauge®) is given by: 
M xX + G(x) = F(t) (I-1) 
where; 
M = equivalent mass of moving system 
x = deformation of the ball = displacement of the piston 
" 2 
33 ax = acceleration of associated mass M 
at 
G(x) = the "force function", i-e-, the opposing force at deformation x 
F(t) = "driving function”, i-e-, applied force as a function of time t. 
In the case of the ball crusher gauge, it has been shown®» > ¢) that, 
within certain limits, the force function is linear, allowing G(x) in 
Eqe (I-1) to be represented by 
G(x) 
kx (I-2) 
The equation of motion then becomes 
Mx + kx 
F(t), (I-3) 
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