# Degree of Freedom¶

## Example 1. 3D Harmonic Oscillator¶

If the oscillator has no transitional and rotational degrees of freedom, but it has 3 vibrational degrees of freedom, then the energy is

$$\large \begin{split} E &= \text{(kinetic energy)} + \text{(potential energy)} \\ \\ &= \left( \frac{1}{2}kT \times 3 \right) + \left( \frac{1}{2}kT \times 3 \right) \\ \\ &= 3kT \end{split}$$
• GRE Physics GR0177: Problem 005