To ensure that doors return to their closed positions, springs are commonly attached to them. However, with this spring the door may swing back and forth several times. For this problem, analyze a door 1 meter wide and 2.25 meters tall, with a mass of 22.7 kg (50 lbm). The mass moment of inertia of the door about its hinge axis is calculated to be 7.57 kg-m2.

a) Draw the free body diagram for this system and derive the equation of motion for the door and spring system. We will analyze the response of the door when subjected to a short, hard push which can be modelled as a unit impulse. Include this pushing force in your EOM.