MOTION OF DEVELOPABLE CYLINDERS. 



85 



A denoting the constant. If this be determined by the 

 supposition that the mass starts from rest, the equation 

 may be written as follows : — 



(dx\ ig . *" 



( -^ ( =— sin airW-- 



ex 

 I— 



or, if / denote the length of the tape, 



f oc 



(dx\ 2 . *' 



I — ) = - q sin at 

 \at) V 



x 



Hence as x approaches to the value I the velocity increases 

 indefinitely. The whole tension at the fixed point at any 

 time will be 



' /' x\^ 



i I+ ( I_ r) 



M<7 sin a—gM l sin -a — ^ — . 



3 K) 



The initial tension will be — — . 



3 



If the external end of the tape were attached to the 

 contiguous coil so that it could not unroll, the tension at the 

 fixed point would be M^ sin a. If the fastening suddenly 

 gave way, the tension would immediately alter and become 

 only one third of its previous value. 



If we suppose the length of the tape to be infinite, 

 then the velocity after describing any finite space will be 



v 



sin a . x. 



