456 BELL SYSTEM TECMNtCAL JOURNAL 



nair- nirx 



rdui 

 Idti'- 



The first and second conditions state that the displacement and velocity of 

 every point in the bar must be the same at the beginning of the second inter- 

 val as at the end of the first interval; the expressions in (4.3.18) and (4.3.19) 

 are obtained from (4.3.10). The third condition prescribes the constant 

 velocity of departure from the floor of the mass ntn and, therefore, of the 

 end of the bar attached to it. The last condition states, again, that the 

 strain at the free end of the bar is zero. 



It may be verified that a solution of (4.3.4) satisfying conditions (4.3.18) 

 to (4.3.21) is 



^ mrx /nirat' \ 



vt' -\- 2^ Cn sin — - sin I ^t" + 7„ 1 



{t' ^ 0, / ^ 7r/w2), 



(4.3.22) 



where 



^vt sin - ~ 

 Cn sin 7„ = j -/^ ^v2 =1 (4.3.23) 



(nair\ 



■K an 



mra 



