How to find the average potential energy given V(x,y) and E?

[dwellexity]

Homework Statement

A classical particle with total energy E moves under the influence of a potential V(x,y) = 3x³+2x²y+2xy²+y³. What is the average potential energy, calculated over a long time?

Homework Equations

The Attempt at a Solution

I think that this can be solved using Virial Theorem but I am unable to apply the standard form 2T = nV. What is the value of n here?

 

[haruspex]

Homework Statement

A classical particle with total energy E moves under the influence of a potential V(x,y) = 3x³+2x²y+2xy²+y³. What is the average potential energy, calculated over a long time?

Homework Equations

The Attempt at a Solution

I think that this can be solved using Virial Theorem but I am unable to apply the standard form 2T = nV. What is the value of n here?

Perhaps I'm being too simplistic, but I note that the potential function has no lower bound and no local minima, so...