Prove that, for any system in equilibrium with a reservoir at temperature T, the average value of the energy is 1 az z aB E = In Z, where B = 1/kT. These formulas can be extremely useful when you have an explicit formula for the partition function.

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Q: 4. Show that functions (a) x = A sin wt, (b) x = A sin wt + B cos wt, (c) x = A cos(@t + ¢)

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