The mechanism shown is composed of a thin rod of length L and mass m, and a vertical slider, which also has mass m. The mechanism has a massless, frictionless roller at point A that maintains contact with the horizontal ground at all times. The vertical slider is connected to rod ABC with a frictionless pin at point B. The mechanism is lifted by a constant force F that acts perpendicular to the rod at end C. Additionally, there is a spring of stiffness k that is undeformed when the rod ABC makes a 30 angle with the horizontal. Answer the following questions, using as the generalized coordinate. (a) Give an expression for the kinetic energy, T, in terms of and 8. Recall that the centroidal moment of inertia of a slender rod is mL/12. (b) Give an expression for the potential energy, V, in terms of 0. (c) Give an expression for the generalized force, Q, resulting from the applied force F. (d) Use Lagrange's equations to find the equation of motion for the system in terms of 0. F C L/2 www B 0 L/2 m A T = mL0cos0+ mL0; v = mgLsine + kA; A= =(sine - 0.5); Qe=FL(sin(0)+2cos (0)) 24