404 BELL SYSTEM TECHNICAL JOURNAL 



2.7 Influence of Dry Friction on Acceleration and Displacement 



By "dry friction" is meant friction that is independent of velocity except 

 for sign. During contact of the package with the floor the motion of W2 

 might be opposed by a constant friction force F. Such a force is developed, 

 for example, in a package with corrugated spring pad cushioning by rubbing 

 against the side and end pads in a top or bottom drop. A typical ideaUzed 



2F 



Fig. 2.7.1 — Load vs. displacement for cushioning with dry friction. 



load-displacement curve is shown in Fig. 2.7.1. For the first downstroke 

 of m^ , the equation of motion of m^ is 



W2X2 + ^2^*2 = —F. 

 With initial conditions 



the solution of (2.7.1) is 



Xo = 



]/dl+ (IJ sin i..J + a)- I 



(2.7.1) 

 (2.7.2) 



(2.7.3) 



where 



