Consider a one-dimensional classical harmonic oscillator (a) sketch the trajectory in the phase space for the representative point for this oscillator (b) consider now an ensemble of these oscillators in which the initial phase is random, but uniformly distributed in the interval [0, 27]. show that the system is ergodic. [hint: explore the condition for time averages being equal to averages over the ensemble.]

7.study the scenario. a small container of water with a low temperature is poured into a large container of water with a higher temperature. which choice correctly explains what happens to the thermal energy of these systems? the smaller container of water has more heat and thermal energy than the larger container. some heat and thermal energy is transferred to the larger container of water. the larger container of water has more heat and thermal energy than the smaller container. some heat and thermal energy is transferred to the smaller container of water. the larger container of water has more thermal energy and some of that energy is transferred to the colder water in a process known as heating. the smaller container of water has more thermal energy than the larger container, and some of that energy is transferred to the warmer water in a process known as heating.