Elastic stability and buckling

If one writes C =FIEI, the following diflerential equation is obtained. 

The solution for the equation has the form T=wsinCx+ cosCx. The strut is symmetric about x=0 and this is consistent with the cosine term (m=0). Denoting the maximum deflection as and noting that T=0 at x= LI2, one obtains YqCos(CL/2)=0. For 0, this is satisfied if CL= n to give 

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