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 , ω₁,ω₂ vs. P'.