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yxgao
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Why does the half of a harmonic oscillator potential allow only odd values of n?
Thx
Thx
yxgao said:Why does the half of a harmonic oscillator potential allow only odd values of n?
Thx
A half harmonic oscillator is a type of system in which the restoring force is proportional to the displacement from equilibrium, but only for one half of the motion. This means that the system oscillates with a decreasing amplitude over time, rather than maintaining a constant amplitude.
Some examples of half harmonic oscillators include a pendulum with air resistance, a child on a swing, and a mass attached to a spring with a dashpot (a device that provides resistance to motion).
Yes, the frequency of a half harmonic oscillator can be changed by altering the characteristics of the system, such as the mass, spring constant, or damping coefficient. However, the frequency will always be proportional to the square root of the spring constant divided by the mass.
The main difference between a half harmonic oscillator and a full harmonic oscillator is that the restoring force in a full harmonic oscillator is proportional to the displacement for the entire motion, while in a half harmonic oscillator it is only proportional for half of the motion. This results in different patterns of motion for the two systems.
Half harmonic oscillators are studied in various fields of science, including physics, engineering, and biology. They can be used to model and understand the behavior of complex systems, such as molecular vibrations, electrical circuits, and animal locomotion. Additionally, half harmonic oscillators have practical applications in fields such as seismology and earthquake engineering.