402 



BELL SYSTEM TECHNICAL JOURNAL 



0.1 0.2 0.3 4 0.5 0.6 0.7 0.8 9 1.0 

 ^2 (FRACTION OF CRITICAL DAMPING) 



Fig. 2.5.3 — Influence of velocitj' damping on maximum acceleration. See ecjuation (2.5.5) 



Then, from (2.5.5), at / — 



and, after / = 0, 



Go 



= 2)32 



„—^2"2ti 



(2.5.7) 



(2.5.8) 



(2.5.9) 



where /„, , the time at which the maximum occurs, is given by 



tan .,/., Vl - ft = ^,(3 _ 40=) ' 



The largest value of G,n/Go from (2.5.7) and (2.5.8) is plotted against ^82 

 in Fig. 2.5.3. It is shown there that, as the damping is increased from zero, 

 the maximum acceleration first decreases to a minimum of 80% of Go and 

 then increases to Go at 50% of critical damping. In this interval the maxi- 

 mum acceleration occurs after / = 0. For damping greater than /S2 = 

 0.5 the maximum acceleration occurs at the instant of contact and increases 

 in direct proportion to 02 ■ 



2.6 Influence of Damping on Rebound 

 In considering rebound without damping, it was found that rebound does 

 not occur unless the product of the maximum acceleration and the sus- 



