. Problem 5 load. This is the discrete version of the beam buckling problem and it is also similar in configuration to a double The figure shows a two degree of freedom model for buckling of a column that is subjected to a follower k. The links support the discrete particles 2m and m at the positions shown. The absolute coordinates 01 and 02 give pendulum. Two massless links, each of length L, are connected and affixed to ground by torsional springs of stiffness the orientations of the rods. Ignore the small effect of gravity. By using Lagrange's equation, derive the equations of motion, noting that P is non-conservative. [4 pts] Linearize the equations of motion about 01 02 0. Are the mass and stiffness matrices symmetric? [4 pts] Define the dimensionless time and load parameters: t= equation of motion. k mL t and p PL and non-dimensionalize the k [4 pts] Show that solutions of the form ue must be such that the eigenvalue is a root of the characteristic equation 22+(7-2P) + 1 = 0. [4 pts] can be complex. Over what load range is the system stable (2 imaginary)? Over what ranges do flutter (2 Discuss the behavior of the roots over the load range 0 < P' < 10, taking into account the possibility that they complex with positive real part) and divergence (a real and positive) instabilities occur? [4 pts] 5. em L k Discrete model of a column subjected to a follower load.