- #1
McLaren Rulez
- 292
- 3
Homework Statement
A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. The average total energy of oscillator is
A. ½kT
B. kT
C. ³⁄₂kT
D. 3kT
E. 6kT
Homework Equations
Equipartition theorem
The Attempt at a Solution
So I know the answer is D. The justification given is that a harmonic oscillator has two degrees of freedom (##1/2kx^2## and ##1/2mv^2##) in each dimension so 6 degrees of freedom. The equipartition theorem assigns ½kT to each.
I don't understand why the ##1/2kx^2## and ##1/2mv^2## are independent degrees of freedom. Aren't they related by the total energy in that dimension i.e. ##1/2kx^2 + 1/2mv^2 = constant##? Thank you.