Determine the critical load, Electrical Engineering

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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 EIy , The column is modeled with three elements of equal length.

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(a) Determine the critical load Pcr at which the column becomes dynamically unstable.

(b) Plot Re(λ) vs. P'.

(c) Plot , ω12 vs. P'.


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