TRANSIENTS IN MECHANICAL SYSTEMS 



677 



placement of .42 times the peak pulse amplitude or approximately f inch 

 may be expected. 



Taking into consideration that the shock mount has been designed with a 

 certain amount of damping, it is thus possible to hold the relative displace- 

 ment within the boundaries of its shock-absorbing capacity. 



Fig. 12 — System with damping. 



Viscous Damping 



The fundamental differential equation for a system with damping is (see 

 Fig. 12). 



x+ 2fx-\- (/x = 

 If we let a whip operate on this system we obtain 



X + 2tx + CC'^X = 03^Xi{t) 



(25) 



(26) 



However, the sudden displacement of the base also produces an acceleration 

 of the mass proportional to the velocity. If Xi(t) is the displacement then 

 Xi{t) may be represented to be the velocity and 2txi(t) the acceleration. We 

 have, then, for the completed equation 



x-\- 2tx + oy'x = Jxiit) + 2txi(t) 

 In the Laplacian terminology, if 



xiiO = Fis) 



(27) 



