664 • • BELL SYSTEM TECHNICAL JOURNAL 



then 



— = ao = acceleration, 



ah , 



V = — = aQO 



Ml 



For a 2000-ft. pound shock the table speed v is approximately 7 ft./sec. 

 Substituting, we find for ao or the acceleration 



7 = aoX .00005 ' 



or flo = 140.000 ft./sec.2 



flo = 4400 "g"s 



This is about the order of magnitude which the accelerometers have 

 recorded. 



The important conclusion we draw from this is that the acceleration and 

 its time interval combine to produce a velocity of the base which is a com- 

 plete criterion of the severity of the shock administered. 



In the example just cited the weight of the table is approximately 800 lbs., 

 and the force 4400 x 800 = 3,250,000 lbs. The result is, then, that a tri- 

 angular impulse of 3,520,000 lbs. magnitude and a duration of 100/xs operat- 

 ing on a table of 800 lbs., imparts to that table a velocity of 7 ft./sec. 



PART II 



Analysis or the Response 



In Part I the origin of the motion of the base has been treated. This mo- 

 tion of the base can now be represented by a pulse or a displacement as a 

 function of time. To distinguish the displacement-time function from the 

 force-time function, we have already suggested the name Whip. Obviously 

 some of the pulse shapes which were used to represent impulses are not suit- 

 able as whips. For instance, the square pulse as whip could not exist, since 

 this would suppose an infinite velocity. 



The triangular whip is observed in the medium-high-impact shock ma- 

 chine. The sine whip may be taken to represent approximately the output 

 of the light-high-impact machine. 



The shifted cosine whip is sometimes used in the motion of cams of auto- 

 matic equipment. 



The problem of shock response is now reduced to the behavior of a mass 

 and spring system when the base motion is represented by a whip. 



