MOTION OF AN OSCILLATING ROD. 159 



The ring exhibited by Dr. Joule had three cords; to 

 simplify the solution I suppose that there are only two, 

 both in the plane of motion, also I suppose that the mass 

 of these cords is so small that the tension due to their own 

 weight may be neglected, and that the cords are uniformly 

 stretched. 



To determine the position of rest let T denote the ten- 

 sion in each of the cords supporting the rod, t l the tension 

 in the upper cord of the damper, t x the tension in the 

 lower cord; then 



i»0r-2T-f x + * a =o, (i) 



rn l g + t 1 ~t 2i = (2) 



Let L be the unstretched length of cords supporting the 

 rod, L r the stretched length, / the unstretched length of 

 the cords attached to the ring, /, the stretched length of 

 the upper cord, l z the stretched length of the lower cord ; 

 then 



T=£(L,-L), (3) 



t,=}(l-l), (4) 



h=j(k-l) (5) 



Also we have the relation 



l^l z =D-d (6) 



Let ~L Z be the distance of the centre of the ring from 

 the fixed beam ; then we have 



l t =Jj s -I* % +2' (7) 



l^h-h^-d (8) 



