5. DIFFERENT CONDITIONS AT x » 



Suppose now that the strings are each stretched to tension T, 

 but are joiaed by a mass m whicn is free to slide on a smooth wire 

 perpendicular to the strings. Th* condition of continuity of displace- 

 ment of the siring remains in force, so that as in (2.24) 



y(O-) + 1 - y(0+) (5.1) 



while the equation of motion of the particle is 



T S ((H) " *h (y + e +ik ° X) (0-) = -mo 2 y(0+) (5.2) 



since y(0+)e is the particle displacement. We now find that it it. 

 impossible to eliminate all of y(0±), y' (0±) from the equations (2.18) , 

 (2.20), (5.1), and (5.2), which are statements of the equationsof 

 motion and the boundary conditions. The simplest W-H equation one can 

 get, replacing (2.26), turns out to be 



K(s) Y (s) + Y (s) - -L— + ^ y<°*> (5.2) 



+ - S + k T s 2 _ k 2 



containing two unknown functions, Y + (s), and the unknown constant 

 y(0>) also. Supposing y(0+) ware known, however, we proceed as before. 

 The additive split of i/(s + k ) K_(s) » G + (s) + G_(s) has been given 

 in (3. A); for the other term in (5.3) we proceed in a similar fashion 

 and get 



^ 2 y(o») 



T (s 2 - k 2 ) K_(s) 

 where 



H + (s) + H_(s) (5.4) 



23 



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