The identical uniform slender bars of mass, m, and length, L, in the figure are free to rotate from their pivot points. Assume small displacements. a) Use Lagrange's equations to derive the equations of motion parametrically using, 0, and 82, as the generalized coordinates. b) Calculate the natural frequencies and mode shape vectors of the system. Illustrate the mode shapes by drawing sketches for each. (For this part only use m = 1 kg, k = 10 N/m, L = 1m, a = 0.7m) L Lim A 2k mn Identical slender bars of length L. mass m 24 +