Exploring Potential Energy in Oscillating Systems

[romantichero7]

1. With respect to any oscillating system, what is the difference between ΔPE, PE, and PEaverage?

Homework Equations

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The Attempt at a Solution

Hi all. I want to preface this by saying that we have been discussing the Lennard-Jones potential and particle theory in class recently, after learning spring-mass potential energy dynamics.

So I was thinking, ΔPE is the change in potential energy from some initial point to some final point.. so it is really a measure of CHANGE in the potential to do work...

I was thinking that plain PE is like the instantaneous potential energy at a specific point in the oscillation.. and it is often arbitrary based on where we set our coordinate system.

I struggle with PEaverage because it is not a term we have used in class before; but my attempt is that it is just the mean value of potential energy over some stretch of time.

What do you guys think?

 

[lightgrav]

yes, ΔPE is some particular change, as the object moves to a new location.
PE for a spring-with-mass system is usually measured from the spring-not-stretched location, since PE=0 there (and is always positive).
PE for an atom-style potential (L.Jones, et.al) are always measured from infinity, since PE=0 there.
PE average is most convenient to average over one oscillation ... they're all the same unless there is dissipation (friction),
but if there IS Energy loss to somewhere, you can define ΔE per oscillation (or Q = Eaverage/ΔE per osc)
In L.Jones shallow well, the PEaverage is a bit above the local minimum in that well, due to thermal Energy.

Have any specific questions or doubts?