Harmonic Oscillator and Total Energy

So, when we add ##E_\mathrm{vibration}## and ##E_\mathrm{rotation}##, we are already accounting for the potential energy associated with the restoring force. This is because Hooke's Law applies to everyday objects like a mass on a spring, but when considering molecules, we need to include both vibration and rotation energies. In summary, the total energy of a harmonic oscillator is given by the sum of vibration and rotation energies, as the potential energy associated with the restoring force is already accounted for in these energies.
  • #1
RedDanger
11
0
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

Instead of:

TE = Evibration + Erotation - (1/2)kx2
 
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  • #2
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
RedDanger said:
Then for the total energy of a harmonic oscillator, why is the TE:

TE = Evibration + Erotation

Instead of:

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

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

Related to Harmonic Oscillator and Total Energy

What is a harmonic oscillator?

A harmonic oscillator is a system that exhibits periodic motion, where the force acting on the system is proportional to its displacement from a fixed equilibrium point. Examples of harmonic oscillators include a mass on a spring or a pendulum.

What is the equation for the total energy of a harmonic oscillator?

The equation for the total energy of a harmonic oscillator is E = 1/2 * k * x^2, where k is the spring constant and x is the displacement from the equilibrium point. This equation represents the sum of the kinetic and potential energy of the system.

How does the total energy of a harmonic oscillator change over time?

The total energy of a harmonic oscillator remains constant over time, as long as there is no external force acting on the system. This is due to the conservation of energy principle.

What is the relationship between the amplitude and energy of a harmonic oscillator?

The amplitude of a harmonic oscillator is directly proportional to its energy. This means that as the amplitude increases, so does the energy of the system. Similarly, if the amplitude decreases, the energy also decreases.

How does the mass and spring constant affect the total energy of a harmonic oscillator?

The total energy of a harmonic oscillator is directly proportional to the mass and the square of the spring constant. This means that a higher mass or a higher spring constant will result in a higher total energy for the system.

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