122 Mr. Morrow on Lateral Vibration of Bars of 



Let d = constant, and b = Ax. Equation (4) then becomes 



(to 2- El 



2 ^ 3 I #< 



by virtue of CI) and (5). 



■"' ~ y= l^l' 122 ' 619 ' 04 ^-"17.3,469,38 ?* + -083 d 



-•03* + -000,850,34^) 



-- =4*0/ <67— 7 , • 

 */i ^ 



In the next approximation the differential equation re- 

 duces to 



-g = — |S?^ ; ('020,436,51 ZV-014,455,78 ZV 



+ •001,984,13 ^ 6 --000,59523y +-000,007,73^); 



whence 



- y = '~^p^ (-240053 Z 8 - -340800 ft* + -170304 ZV 



- -072279 ZV + -003543 ar 8 - '000827 y + -000006^) 



f- =4-256 /4 , 



•.Ed 2 



and n=»^ 



All clamped-free bars in which the depth is constant and 

 the breadth proportional to the distance from the free end 

 will vibrate with a period which is independent of the breadth 

 at the fixed end (that is of the value of A), as given by the 

 above formula. 



7. Clamped-Free Bar of Varying Breadth. (b = Ax\) 

 (Pi/ _ Up 



Here d 2 u l'2p y\ C x 2/ N , 



~ 2 (x— z)y dz 



= ^^ 2 --8t+-07142857^) 



