Spring energy and thermal energy connection with unknown force

[superwolf]

I've got no idea where to start here, since f is not known...

 

[Mapes]

I would think you'd want to relate the spring energy, $\frac{1}{2}k\langle x^2 \rangle$ (where $k$ is the stiffness), to the thermal energy, $k_B T$ (where $k_B$ is Boltzmann's constant).