THE RANKINE-GORDON FORMULA 868 



Then 2-653(226-8 + x 2 ) = 625 - x* 

 x* + 2-65ar 2 = 23-4 

 x 9 + 1-827 = 5-016 

 x 2 = 8-689 

 x = 1-921 



(2) When the ends are fixed, 

 36 



= 1-52 x 10- 4 



471* x CUUO 



MA 



and 



x 6000 



300 36 



7t(25 - x 2 ) 50-45 



25 + x 2 



= 36(25 + x*} 

 75-45 + x 2 



Then 2-653(75-45 4- x 2 ) = 625 - x* 



x* + 2-QSBx 2 = 424-8 

 x 2 + 1-327 = 20-65 

 x 2 = 19-32 

 x = 4-395 



(3) When one end is free and the other fixed. 

 36 



= 2-97 x 10- 4 

 J-U477C a x 6OOO 



MM 



and 



2-04771 2 x 6000 



300 36 



7t(25 - X 2 ) 98-56 



25 + x 2 



_ 36(25 + x z ) 

 " 123-6 + x 2 



Then 2-653(123-6 + x 2 ) = 625 - x* 



x* + 2-Q53x 2 = 297-2 

 x 2 + 1-327 = 17-30 

 x 2 - 15-97 

 x = 3-996 



183. Damped Vibrations. A body of mass m Ib. is suspended 

 from a spring of stiffness h that is, a force of 1 Ib. will extend the 

 spring by h feet. The body is displaced from its position of 

 equilibrium and then allowed to oscillate in a resisting medium, 

 the resistance of which is proportional to the velocity of the body, 



