[ 2 -1 0 ... 0 0 0]
[-1 2 -1 ... 0 0 0]
A=[ ... ...]
[ 0 0 0 ... -1 2 -1]
[ 0 0 0 ... 0-1 2]
The eigenvalues of this matrix will all be real and positive. (Use Matlab/Octave)
For n sufficiently large, each eigenvalue λ of A can be used to approximate a critical load
P=Rλ/h²
under which buckling may occur.
The most important of these critical loads is the one corresponding to the smallest eigenvalue since the beam may actually break after this load is exceeded.