Movement of an object inside a bowl

[Walker2]

Homework Statement

The problem consists of finding a set of 2 differential equations describing the motion of a round object moving inside a 2D-bowl, of equation y=x^2. Only data given is that the equations have to be in the form of :
(x1)'=x2, and
(x2)'=f(x1,x2,weight of object, gravitational acceleration, K=constant of friction).
The constant of friction is used to determine the friction between the object and the bowl.
The main issue here is to find f.

Homework Equations

The curve of the bowl : y=(x1)^2.
(x1)'=x2,
(x2)'=f(x1,x2,m,g,K).

The Attempt at a Solution

After long days of reflection, I haven't managed to come up with an intelligent attempt at the solution. Please push me in the right direction!

Thank you!

 

[lanedance]

how about stating with an FBD (free body diagram) of the object with all the forces at play for some arbitrary x

also i assume we assume the object is always sliding within the bowl... (ie not rotational considerations)

 

[lanedance]

you can probably choose x1 & x2 tobe whatever you want... though the obvious choice would be x1 = x, then x2 = x1' is the horizontal velocity & x2' is the horizontal acceleration which must be in balance with the forces at play...