680 BELL SYSTEM TECHNICAL JOURNAL 



of the whip by v the expression for x may be formed from equation (7) by 

 setting / < h. 



t< b (37) 



(38) 



(39) 



VCO 



By proceeding in a similar manner with the next step of the whip the value 

 of the acceleration ratio will be found to be 



Xo = 3 



and for the completed whip or steady state 



Xo= 4 



The expression ^o = Xofco is an important factor in shock considerations. 

 Thus we have a simple relation for the final maximum amplitude of the periodic 

 acceleration of the mass m when subjected to a triangular whip; viz., it is 

 four times the product of whip velocity and natural frequency of the system. 

 The constant Xo depends upon the configuration of the whip; the velocity 

 V indicates the intensity of the whip; while co expresses the kind of response 

 the system is capable of. 



It is of interest to note that this maximum periodic value of ^o will be pro- 

 duced only if the ratio of pulse frequency and natural frequency is of the 

 correct value. It is difficult to produce shocks on existing equipment of 

 exactly the same characteristics within narrow limits as to time duration 

 and therefore it must expected that a considerable variation in damage 

 may occur even though similar shocks are administered to identical test 

 objects. For the same reason a shock of lower intensity may produce 



