A pendulum of length l and mass m hangs from a bead of mass M that moves frictionlessly along the curve y=x^4 . Use y, the height of the bead above its lowest point, and θ, the angle of the pendulum with respect to the vertical, as the generalized coordinates,
(a) Find the Lagrangian of the system.
(b) Find the Lagrange's equations of motion.
(c) Simplify the equations of motion in case both coordinates are very small.