2. A pendulum of mass 5.1 kg, length 3.2 m and an air resistance coefficient of 5 Nsm-1 is released from an initial position in which it makes an angle

of 25° with the vertical. a) Assuming that this angle is small enough for the small-angle approximation to be made in the equation of motion, solve the second order ODE that would describe the pendulum's motion. (5) b) Identify the dampening coefficient for this system and explain what this means physically. (2) c) How long will it take for the amplitude of the motion to have fallen to less than 5% of the initial amplitude? Justify your method used.(3)