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

  1. Dec 1, 2018 #1
    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.
  2. jcsd
  3. Dec 3, 2018 #2
    p ~ exp(-E/kT), E ~ omega^2
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