Exercises: 6.2 (A9 only), 6.4 (A3, A5 and A6 only).

Project Problem: This problem starts the theoretical work you need to do for the pendulum project. Determine the equation of motion for a pendulum of length

*l*with a mass attached to the end with mass

*m*as illustrated in the following figure where tau is an applied torque. Is the equation linear or nonlinear? If the angle is small so that you can assume sin(t) is approximately t, if you replace any sin(theta) by theta and any cos(theta) by 1, is the resulting equation linear or nonlinear? Using the same assumption (small angle) what is the equation if the angle is zero when the pendulum is hanging straight down instead of up?