Harmonic Oscillator and Total Energy

[RedDanger]

Okay, so if a harmonic oscillator has a restoring force given by Hooke's Law such that

F_s = -kx

and its integral gives the potential energy associated with the restoring force:

PE = -(1/2)kx²

Then for the total energy of a harmonic oscillator, why is the TE:

TE = E_vibration + E_rotation

Instead of:

TE = E_vibration + E_rotation - (1/2)kx²

 

[TheNutyProfesr]

hookes law applies to everyday objects like a mass on a spring,
I assume that when you speak of vibration and rotation energies you are considering a molecule?
If so, then 1/2KX^2 = E vib + E rot

 

[DrClaude]

Then for the total energy of a harmonic oscillator, why is the TE:

TE = E_vibration + E_rotation

Instead of:

TE = E_vibration + E_rotation - (1/2)kx²

Because the $kx^2/2$ term is included in $E_\mathrm{vibration}$.