Phonon density of states of a 1-d linear chain

The phonon density of states of a 1-d linear chain is,

The form below generates a table of where the first column is the angular frequency ω in rad/s and the second column is the density of states D(ω) in units of s/(rad m).

The density of states can be used to calculate the temperature dependence of thermodynamic quantities.

• Energy spectral density u(ω)
• Internal energy density u(T)
• Specific heat c_v(T)
• Helmholtz free energy density f(T)
• Entropy density s(T)