126 



SuDstitutin^ fron equation (11) in equation (7) we firit) after integration that the total 

 kinetic energy T is given by 



«^"^-"[^^^s-'(a^"T 



0-2) 



We find sirr.ilarly, by substituting fr-jm equiition (11) in equation (10), that the total 

 potential energy V is given by 



V =Jk, u ♦ikw- 



i^^T^ 



F (t) 



(13) 



6110 (".Slifa^ t bM + 20^ 1 

 at) |_ 1575 [ b' "? J IIO25J 



(11) 



By definition L = T - v and applying equation (2) by taking q = u and q = w we obtain the 

 equat ions 



(V) + M.) u 4. -21 n w + k u = F (t) 



1 75 e; *■ 



225 [ 315 J 



225 



F (t) 



(15) 



which together with the initial conditions 



w = w 



suffice to determine u and w as functions of t. 



The solution of equations (15) is elementary and needs no ccmments, but it is instructive to 

 conpars this solution with that for a double system composed of a mass on a spring supported on a 

 second mass on a spring as shown in Figure 2, 



