A pendulum consists of a mass m suspended from a fixed point by a string of length b. The pendulum is immersed in a viscous medium, which exerts a retarding force proportional to the velocity. The proportionality constant of this retarding force is 2m√/g/b, where g is the acceleration due to gravity. a) Draw a free body diagram. b) Using Newtonian approach, write differential equations describing the motion without assuming a small-angle approximation. c) Assume that the pendulum is initially released from rest at a small angular displacement a from the vertical. Find expressions for the angular velocity and angular displacement of the pendulum at a later time under the small-angle approximation.

A pendulum consists of a mass m suspended from a fixed point by a string of length b. The pendulum is immersed in a viscous medium, which exerts a retarding force proportional to the velocity. The proportionality constant of this retarding force is 2m√/g/b, where g is the acceleration due to gravity. a) Draw a free body diagram. b) Using Newtonian approach, write differential equations describing the motion without assuming a small-angle approximation. c) Assume that the pendulum is initially released from rest at a small angular displacement a from the vertical. Find expressions for the angular velocity and angular displacement of the pendulum at a later time under the small-angle approximation.