Probability at a temperature T that a system has a particular energy

[Hector Triana]

Salutations, I'm starting in statistical mechanics and reviewing some related studying cases I would like to understand what occurs in small systems with normal modes of vibration, for example, a small system that has 2 normal modes of vibration, with natural frequencies $$\omega_1$$ and $$\omega_2=2\omega_1$$. So, what would be the probability at a temperature T that the system would get an energy less than $$5\omega_1/2$$? if it's assumed the zero of energy is taken as its value at $$T=0$$
I would like any guidance for better understanding of that kind of cases because those problems are very interesting, specially how to approach them.

Thanks for your attention.

 

[Dr Dr news]

p ~ exp(-E/kT), E ~ omega^2