Calculating the Period Time of a Ball Inside a Ball

[asi123]

Homework Statement

As you can see, I have a ball inside a ball.
One with a density p1 and the other p2.
the ball stand on a surface with friction so it can move without sliding.
they move the ball from its rest point and release it.
I need to figure out the period time, any idea?

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

As you can see, I have a ball inside a ball.
One with a density p1 and the other p2.
the ball stand on a surface with friction so it can move without sliding.
they move the ball from its rest point and release it.
I need to figure out the period time, any idea?

Hi asi123!

(is there zero friction between the balls?)

The only way to approach this is to work out the equations of its motion first.

Hint: lots of things are being conserved.