Solving the Frequency of Small Oscillations in a Spherical Dish

[S0C0M988]

A marble of radius b rolls back and forth in a shallow spherical dish of radius R. Find the frequency of small oscillations. You can solve this problem using conservation of energy or using Newton’s second law. Solve it both ways and show that you get the same answer.

I kind of get the concept and I'm using conservation of energy but he numbers don't work out. I know the answer is supposed to be w^2 = 5g/7R

I set up PE = KE + Rotational KE but it doesn't work.

 

[OlderDan]

A marble of radius b rolls back and forth in a shallow spherical dish of radius R. Find the frequency of small oscillations. You can solve this problem using conservation of energy or using Newton’s second law. Solve it both ways and show that you get the same answer.

I kind of get the concept and I'm using conservation of energy but he numbers don't work out. I know the answer is supposed to be w^2 = 5g/7R

I set up PE = KE + Rotational KE but it doesn't work.

It worked for me except I have R - b instead of R. Assuming a small marble. R is close enough.