TRANSIENTS IN MECHANICAL SYSTEMS 681 



more damage than a higher one because impulse amplitude as well as dura- 

 tion change at the same time. 



Although damping is a highly desirable feature in a shock mount, the 

 damping device may cause a certain amount of coupling between the mass and 

 the base, and if too much damping is provided the transient acceleration of 

 the mass may become excessive. 



The analysis of this problem by means of the Laplace transforms is not 

 difficult, for we can use results previously obtained. The transform equa- 

 tion for a system with damping, subjected to a whip, is 



w2 + 2as 



in which F{s) represents the transform of the disturbance or excitation. 

 Since we are interested in the effect of the damping or rj upon the response, 

 only the first part of the triangular whip will be considered. 



In this case 



Xi(t) — vl 



and 



iS[xr(t)\ = F{s) = '-. (41) 



Substituting (41) in (40) 



v(o3^ 4- las) 



If X(s) is the transform of x{t), a displacement, then the acceleration is x(i) 

 or g(t)j (x(t) = g{t) by definition) and 



^[x{t)] = ^\g{t)\ = s'Xs 



Substitution in (42) gives 



2 



s'Xis) = 2va , . ,/^ ,, (43) 



{s + ay + ^ 



Now .£-n^'^(^)l = g(i) 

 so that 



g{t) 



= T [(i " « J + P'] ^-" sin {fit + f ) (44) 



