QUESTION 2 a) The vibratory system in Figure Q2 has three components which are pivoted at O. At the instant represented, the system is in equilibrium position. The 0.5-kg uniform slender rod of 4r. m long is rigidly welded to the 4-kg homogeneous disc whose radius is r. A 1-kg mass is attached to the end of the slender rod. A damper, c, is placed at the center of the slender rod. During the installation of the system, the initial length of the spring was stretched 0.1 m until the equilibrium position was achieved. Derive the differential equation and determine the natural frequency of the system. b) If the system is to be designed so that the motion behaves critically, determine the required damping coefficient, c.. c) When the damper is removed from the system and the initial disturbance is imposed to the system, it is found that the initial displacement and velocity of the end slender rod are 0.05 m and 0 mm/s respectively. Determine the response of the system when t=1.5 sec... D Figure Q2 T