Question

4. A simple classical harmonic oscillator (SHO) consisting of a spring-mass oscillator has an energy spectrum of En = 1nhw. Calculate the partition function of the SHO. Show that in the high-temperature limit (t >>ho), it is approximately Z≈ t/(ho). Then, calculate the internal energy U, specific heat C,free energy F and entropy o. According to the Equipartition Theorem, any degree of freedom in the motion of a classical particle (KE, PE) will contribute an energy (1/2)kT. Based on this, what is the internal energy U of a one-dimensional SHO and compare this with your result in (a).

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