Derive the equation(s) of motion for a particle moving on the inner surface of the parabol...

Derive the equation(s) of motion for a particle moving on the inner surface of the parabolic bowl shown. Assume that the particle only moves in the vertical xy plane that goes through the center of the bowl, that the equation of the parabola is y(x) = 1 + 0.5x2, and that gravity is acting in the −y direction. The bowl’s cross section is shown on the right side of the figure.

Figure P3.63