Linearization Problem: A pendulum hangs vertically from the ceiling, as illustrated below: Where is the mass of the pendulum, is the length of the arm, and is the angle measured from the vertical. 1. Derive a model for the motion this system. Characterize your model as completely as possible. 2. Linearize your model for small values of . Characterize your new model as completely as possible. 3. Solve your linearized model for (), assuming an initial angle of (0) = 0 and an initial velocity (0) = 0. What does this system do as ? Does this make sense physically? Why might we be seeing this result