For the mechanical system shown to the right, the uniform rigid bar has mass m and pinned at point O. For this system: a) Find the equation of motion using Lagrange's Principle and verify using Newton's 2nd Law. b) Identify the damping ratio and natural Bonus: frequency in terms of the parameters m, c, k and /. c) Given the following parameters m -2 kg,1= 25 cm, c-0.25 N s/m and k-50 N/m, find the angular displacement ((t)) of the bar for the following initial conditions: (0)-0 and (0) 10 rad/s k ww d OT aT OR OU + + =2 m