Vibrations of twitched and stroked Strings. 217 



„-A(L-..)r+B:(-5L)(^T-*) 



„ mx—2(i—j-\- 1)L < t_ < 2(i+j)L--mx 

 t0r 2mL =T = 2mL ; 



2mL =T=m 



These equations are to be formed for j=l, 2, 3, .... i; and 

 then the first of them, formed for j=i+ 1, is to be superadded 

 — namely, 



fo r ±<i<«^ 



™=T=2L 



Thereby the first half of the ascending motion is determined; 

 its velocity fluctuates between the values 



and 



A(L-*)+Bg'L-*). 



For the descending motion we find: — 



»m + 20'-1)L < J; < 2(2»+y)L— wmt 

 2mL =T = 2mL 



^(«-')-K^ i -«)(' : ? T -') 



for 2(2^+.y)L-mj? < t < iwg + 2/L 

 2niL = = 2mL 



These equations are to be formed for 



j = I;.2,....m-2*-l, 



and then the first of thorn, formed for jssm—2i is to be super- 



