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A harmonic oscillator follows Hooke’s law, where force is proportional to displacement. A simple example is a block on a spring, with natural frequency f0 and period 1/f0. Damped systems can be overdamped, underdamped, or critically damped. Quantum harmonic oscillators describe molecular interactions using bond strength constants.
A harmonic oscillator is a system in physics that acts according to Hooke’s law. This rule describes elastic behavior and states that the amount of force applied to a spring, or other elastic object, is proportional to its displacement. A system of harmonic oscillators returns to its original position when the force is removed from the elastic object.
In physics courses, a simple example of a block attached to a wall by a spring is often used to illustrate the concept of harmonic oscillation. The surface on which the block slides is assumed to be frictionless. When the system is set in motion, it follows the equation ω0 = 2πf0, which is also equal to the square root of the spring constant (k), divided by the mass of the block (m).
ω0 is the angular velocity, which has units of radians per second, and f0 is the natural frequency, which has units of Hertz. The period of the block – the time required to make one complete cycle of movement – is equal to one divided by f0. The spring constant indicates how stiff the spring is and is unique to each spring. It has units of force per length, for example Newton per metre.
This simple example is called an undamped harmonic oscillator, and he theorizes that because the block moves along a frictionless surface, it will continue to move at the same frequency forever. In reality, however, such a situation would not arise. Real systems with friction are called damped systems, where the motion of the block will slow down, the spring travel will shorten, and the system will eventually stop moving.
A system of harmonic oscillators can be overdamped, underdamped, or critically damped. Differential equations describe the motion of damped systems, so their solution can be quite complex. However, each type of cushioned system has its own type of movement, which is easily recognizable.
In an overdamped system, the block does not oscillate. It slowly returns to its original position after force is applied and the spring stops moving. The block can swing for quite some time in an underdamped system, with the spring stretching less with each consecutive swing until the system returns to rest. A critically damped system behaves in much the same way as an overdamped system, but is optimally designed to return to its original position as quickly as possible.
A quantum harmonic oscillator describes how two molecules interact with each other. They vibrate back and forth similar to a mass on a spring. Instead of a spring constant, the equation for a quantum harmonic oscillator uses a bond strength constant, which describes the strength of the bond between the two molecules. The relationship between angular velocity and frequency is the same.
