The curve y(x) = b(x/a)? is rotated around the y-axis with constant frequency ? (see Fig.). A

Question:

The curve y(x) = b(x/a)? is rotated around the y-axis with constant frequency ? (see Fig.). A bead moves frictionlessly along the curve. Find the frequency of small oscillations about the equilibrium point. Under what conditions do oscillations exist? (This problem gets a little messy.)