102 STRENGTH OF MATERIALS 



Proceeding as in Article 82, the general integral of this equation is 

 found to be _ 



y = A sin (* <J5) + * a ( x N^) + f ' 



in which A and B are undetermined constants.* For x = and /, 



y = 0, and -^ = 0. Therefore, by substituting these values in the 

 dx 



general integral, the following relations are obtained : 



From these conditions, 

 cos 



whence 



and consequently 



T 



which is formula (49) of the preceding article. 



Suppose one end of the column is fixed and the .tli.-r 

 free to turn, and let P k denote the horizontal force neces- 

 sary to keep the free end from lateral movement (Fig. 81). 

 Then the moment at any point C is M = Py P k x t and 

 the equation of the elastic curve is 



general integral of this equation is 



* Calculus, p. 440. 



