669 
| v(t) yp (é—t) dr 
0 
a 
dt? 
Let us now examine in the solution (B) for «(t) when it represents 
a damped motion. A movement will be called damped when the 
limit of the velocity for {== is equal to zero. When we, there- 
from equation (A), may also really be omitted from equation (A). 
' dE Tee ‘ 
fore, first determine the aa from the solution (B) for a(t), we get 
a; 
at once as condition for damping: 
lim w(t) = 0°) 
jie 
lim yp") (t) = 0 
(=n 
The example chosen, i.e. the movement with which from {== — oo 
to ¢=— 0 a force acts equal to zero, and further « and x are zero, 
and then suddenly a. force A that is further constant, so that for 
the movement after the moment zero the equation (A) of p. 668 
is valid, may now also be treated in the special case that we 
att 
assume ws Ae 9 . Equation (A) then passes into: 
t 
Lt 
Las =| a (r) Ae 9 dt + Kk 
0 
aa 
dt? 
By differentiating with respect tot, and by eliminating the integral, 
I derive the equation: 
a a DS eles 
leer WE dn Elger Kran oe en (B) 
The lefthand member of this equation is exactly the same as the 
lefthand member of equation (2) p. 665. When for the moment I 
call this ZL, equation (8) of this page becomes 1 — K, and its general 
solution is obtained by adding to the general solution of L=0O a 
particular integral = K. This is directly found: 
K 
ed 
d 
Further the considerations about damping as they occurred in 
equation (2) on p. 665 now repeat themselves completely. Literally 
the same conditions are written down for damping. 
1) Compare further p. 671. 
43 
_ Proceedings Royal Acad. Amsterdam. Vol. XXIII. 
