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so in this short video what were gonna do is were gonna analyze a column again but this time were going to look at a column which is fixed at one end and free at the other end now were going to derive the equation for the critical load in the column and were also going to derive an equation for the various different buckle shapes or mode shapes for that column now the process is going to be exactly the same as what we went through before first of all were going to determine an equation for the internal bending moment in the column as a function of X in its buckled state were going to set up the differential equation of the deflection curve were then gonna solve the differential equation ad to obtain the general solution then we apply a boundary condition to determine the critical load and the deflected shape of the column were going to look at various different sets of ant conditions and its always going to be the exact same process the exact same steps so what we have here