TRANSIENTS IN MECHANICAL SYSTEMS 



663 



and the final velocity is 





which represents the area of the impulse divided by the mass. 

 Similarly we find for the very short square impulse 



.ri 



= —t 



Ml 



For the square impulse of finite time interval b 



ab 



For the sine impulse 



.ri = 



:*•! = 



nil 



(-0 



LCOo \ ZWo/ 



WlCOo 



For the shifted cosine impulse 



Xi = 



air 



V Wo/ 



(1.12) 



(1.13) 



(1.14) 



(1.15) 



(1.16) 



The velocity is the term preceding the term in parenthesis. 

 In the five examples mentioned, we find that this velocity is proportional 

 to the area of the impulse curve and inversely proportional to the mass. All 



expressions contain the factor — and, since a is the maximum force present, 



this expression represents the maximum acceleration and it is this value 

 which is so frequently mentioned when discussing the actions on the shock 

 table. 



For instance, from records we have determined approximate values for 

 the time interval during which the energy transfer from hammer to the table 

 takes place. The high-speed motion pictures are taken at the rate of 4,000 

 to 5,000 frames per second, which means an average elapsed time of .22 

 milliseconds or 220 microseconds. The energy transfer occurs within this 

 time interval, because the rate of increase of the displacement from frame 



to frame is constant. The exposure time of one frame is second or 83 



microseconds. If the anvil moved within this time there would be evidence 

 of blurring. Since we have been unable to detect any blurring, we may state 

 that transfer is less than 220)us yet more than SO^us. 



Let us assume it to be lOO/us. That means a pulse width of lb = lOO/us. 

 (See Fig. 3.) 



