3. A pendulum with length 1 is attached to the ceiling. It has an attached mass m. The robe is massless. We want to obtain the differential equation that describes the motion (no need to solve it). Make sure to write down all intermediate steps. (a) Use the Newtonian framework to obtain the differential equation describing the motion. (b) Use a single generalized coordinate, and use the Lagrangian framework to obtain the differential equation describing the motion. Indicate the zero of potential energy. (c) Use Cartesian x and y (pointing down) coordinates and the constraint of the pen- dulum rod to derive the equations of motion using Lagrange multipliers. (d) Use a single generalized coordinate and the Hamiltonian framework to describe the motion. Explicitly show that you can combine your first-order differential equations to obtain the same equations of motion.

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3. A pendulum with length 1 is attached to the ceiling. It has an attached mass m. The robe is massless. We want to obtain the differential equation that describes the motion (no need to solve it). Make sure to write down all intermediate steps. (a) Use the Newtonian framework to obtain the differential equation descri