rings in modifying the motion of a I'od suspended from a 

 fixed beam by two cords of slight elasticit}'. in being the 

 mass of the rod and mi the mass of the ring, \^ the modulus 

 of elasticity of the cords supporting the rod, L the length of 

 each cord, X the modulus of elasticity of the cords connecting 

 the rod with the ring, I the un stretched length of each of 

 these cords, then x and Xi denoting the displacements from 

 their positions of rest, of the axis of the rod, and the centre 

 of the ring, the following equations of motion are obtained : 



^ _ 2\ 2\ 



From these equations b}' elimination an equation is obtained 

 of the form 



^^+A^ + Bx = (1) 



dt^ df ^ ' 



. 2AV X \m\ 



■where A = - f + 7 + -, — ) 



m\h I Lnii/ 



Lil 

 Assuming x = Cef^^ 



Differentiating four times, and twice, substituting in 

 equation ( I ) and dividing by a common factor we obtain 



yu* + /A + B = 0. 



On examination all the roots of this equation prove to be 

 imaginar}'-. Substituting trigonometrical functions for the 

 impossible exponentials, an equation is obtained of the 

 following form 



X = Fcospt + Qcosqt + Rsmjit + Ssin^^, 



yfhevep^^-^-^^ -B and q=^~ + ^-^-B. 



The parameters P, Q, K, S, are determined by reference to 

 the initial conditions, and V being the initial velocity of the 

 rod we get the following equation : 



_ V (q^sinpt - 2i*s,mqt) 



