A rocket on a test stand is modeled as a column clamped at x = 0 and free at x = L, and subjected to compressive force P applied at the free end. The direction of load P remains always parallel with the beam axis in the deformed configuration. For simplicity assume that the column is of uniform cross-section with constant EI_{y} , The column is modeled with three elements of equal length.
(a) Determine the critical load P_{cr} at which the column becomes dynamically unstable.
(b) Plot Re(λ) vs. P'.
(c) Plot , ω_{1},ω_{2} vs. P'.