662 BELL SYSTEM TECHNICAL JOURNAL 



For a shifted cosine pulse 



'-« = 27(^.1) (^-^^^"") ''■''' 



Suppose we let an impulse, and to take a specific example, a triangular 

 impulse, operate on a mass mi. We have 



F = wioo (1-06) 



in which 



F = F{t) = force in lbs. 



Ml = mass in slugs 



ao = xi = acceleration in ft/sec 



Let I'lxiit)] = X,{s) = Xi 

 then 



iL[wifi] = Wi6 Xi{s) 



the ii^ transform of a triangular pulse F{t) is 



Substituting 



The inverse transform is 



The solution of 1.09 



^.(0 = ^lK-2 (-'-^' nil ~b)+ '^^ nil - 2b)] (1.10) 

 nil b[_o 6 6 J 



After the impulse is over, i.e., for values of / > 2b, 1.10 becomes 



x,(t) =±b{t- b) (1.11) 



mi 



