22 Prof. Barton and Miss Browning on 



Referring to the end elevation, fig. 3, let the displacements 

 at time t of the bobs P, Q, and R be respectively x, y, and z. 

 Also, let the displacement of B on the bridle cord ABDE 

 (figs. 3 and 4) be u, and that of the point C on the bridle 

 cords A" C" D" E" be w, both at time t. All these displace- 

 ments are reckoned positively if to the right-hand in fig. 3. 

 Then the equations of motion may be written in the form : 



For bob P, 21fj~ + 2% ^ = 



For bob Q, 2 Ji^f -f 2MgV-^ = 



dtf 



z — w 



For bob R, 2M~ + 2Mg —^- = 0. j 



oo 



We thus have three equations involving the five unknown 

 variables x, y, z, u, and w. To reduce these five unknowns 

 to three, we need relations that depend upon the stresses in 

 the bridle cords and bridges. This need involves the tem- 

 porary introduction of two more unknowns, viz. : the force 

 of compression U in the bridge BB' and the tensile force W 

 in the bridge CO". 



Consider, first, the bobs P and Q (displaced x and y respec- 

 tively) and the bridge BB'. Then, since the point B is 

 displaced u, the point B (see fig. 2) will be' displaced ubjb L . 

 This follows from the fact that the position of the bridge 

 when supposed massless reduces to a static problem. And 

 since the bridge BB' is supposed rigid, the displacement of 

 B' is ub/b also. By use of equation (1) these displacements 



, ... 2ud 



may be written -^ 7 . 



d + a — b 



Further, because the cords are supposed massless, the 

 portions EBDP remain in one plane, and therefore the dis- 

 placement of D is found to be 



(x-u)(d-6 ) (x-u)(d-a + b ) 



U "I r 11 -j j . 



a — o b 



Thus we have 



Displacement of D — that of B 



_ (x — u)(d — a+b) 2nd , Q . 



