# Harmonic Oscillator and Total Energy

1. Mar 27, 2013

### RedDanger

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

Fs = -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 = Evibration + Erotation

TE = Evibration + Erotation - (1/2)kx2

2. Mar 28, 2013

### 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

3. Mar 28, 2013

### Staff: Mentor

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