Movement of an object in a bowl

[Walker]

Hey there,

 

There is a homework I have been struggling with recently, and after days of fruitless reflection I turn to the pros at scienceforums.net So, here is the quesiotn : I have to establish a set of 2 differential equations relevant to a round object moving inside a bowl. The bowl can be considered as a 2D curve, of equation y=(x1)^2. I have to find 2 differential equations such as (x1)'=x2, and (x2)'=f(...). The function f must be dependent on the previous values of x1 and x2, as well as the weight of the object, the gravitational acceleration and a constant of friction K. I really have no idea how to do this, a push in the right direction would be extremely helpful.

 

Thank you!!

[swansont]

What is the force on the object, as a function of x and y? This will tell you the motion; you can find the acceleration and velocity, depending on the previous state, which will tell you the subsequent displacement, assuming small increments of time.