50 Mr. J. H. C. Searle on the Effect of 



VII. 1. JPivoted-clamped Bar. 

 f= d cos y-J; + d! sin 7^ + d" cosh y 2 £ + <i' /7 sinh y 2 f • 



Origin at pivoted end. 

 Hence, by (11) 



72/ f when f =0. 



d yi 2 = d"ry 2 2 



d=d"=0. 

 .-. /=d' sin 7l f + d"' sinh y£. . . . (41) 



Also, (io), /=oy z 



0=6^ sin y 1 V-{-d' , [ sinh 7 2 Z' ") 

 and = 7^' cos 7^' + 7 2 cFcosh fy 3 Z' i " 



7i cos 7 1 Z / sinh 7 2 /' = 7 2 sin 7 X Z' cosh 72^, . (43) 

 or 7j tanh7 2 Z , =7 2 tan7 1 Z / (J) 



Substituting from (42) in (41) 



/= Dr^_ s 4^i . . . . (K) 



2. Correction for Rotatory Inertia in a Pivoted-clamped Bar. 

 Substituting for j 1 and 72 in (43) , 



(l-^)sin,(l+| 2 )cosh,(l-y) 



= (l + y)"oosn(l+ ^sinh^l-^, 



( 1 — 7- J(sin n+^j- cos n) (cosh n — ~ sinh n) 



= ( 1 + -T- J (cos ft — sin n) (sinh n — cosh n). 



.*. sin n cosh n— cos n sinh >i 



= — - [cos n smh w -J- sm ft cosh n— 2n cos w cosh n\ . 



or 



