Question

Explain in terms of energy how dissipative forces such as friction reduce the amplitude of a harmonic oscillator. Also explain how a driving mechanism can compensate. (A pendulum clock is such a system.)

Answer 1

Answer and Explanation

The harmonic oscillator strictly obeys the law of conservation of energy. Therefore, the amplitude of the system remains constant.

Dissipative forces, (e.g. friction), result in some energy losses in different forms of energies and results in a decrease in amplitude after each oscillation.

The sum of kinetic energy and potential energy decreases after each oscillation as part of this energy that should maintain the harmonic oscilator in a state of harmonic motion is being used to service friction. If the frictional forces persists, the amplitude keeps decreasing until motion is brought to a standstill.

For the driving mechanism, some external force acting on the system (driving force) must be accounted for and in this scenario, energy is lost due to frictional forces that can be provided back to the system with the involvement of the driving force/mechanism & makes up for the energy lost.

Answer 2

Answer:

There is the conservation of energy in a harmonic oscillator. As a result, the system amplitude will remain constant. The dissipative forces (i.e. friction) lead to loss of energy in different forms and the system amplitude is reduced due to the reduction in both kinetic and potential energies at the end of each oscillation.

The external forces acting on a driving mechanism must be accounted for at all times. In this case, there is a loss of energy because dissipative forces can be returned back to the system in the presence of the driving to account for the loss in energy.

Explanation:

There is the conservation of energy in a harmonic oscillator. As a result, the system amplitude will remain constant. The dissipative forces (i.e. friction) lead to loss of energy in different forms and the system amplitude is reduced due to the reduction in both kinetic and potential energies at the end of each oscillation.

The external forces acting on a driving mechanism must be accounted for at all times. In this case, there is a loss of energy because dissipative forces can be returned back to the system in the presence of the driving to account for the loss in energy.