1. The problem statement, all variables and given/known data From Goldstein Classical Mechanics, 6.16: A mass particle moves in a constant vertical gravitational field along the curve defined by y=ax4 , where y is the vertical direction. Find the equation of motion for small oscillations about the position of equilibrium. 3. The attempt at a solution When taking a quadratic approximation as in the standard way to solve small oscillations, the eigenfrequency vanishes, giving a result without oscillation, which is clearly not what I'm looking for. I'm honestly not sure how to proceed with this.