Types Of Harmonic Oscillator: Exhaustive Insights and Facts

Types of harmonic oscillator are categorized into several types based on their function ability having a back and forth motion which is usually displaced from its equilibrium position that experiences a restoring force.

Types of harmonic oscillator are as mentioned below:

Simple Harmonic Oscillator

A simple harmonic oscillator is one of the types of harmonic oscillator. The back and forth periodic motion from the equilibrium position is also known as simple harmonic motion.

The motion experienced by a system in simple harmonic oscillator is periodic. For example, we consider a pendulum that is suspended from the equilibrium position moves back and forth before coming to rest. The motion back and forth decreases with a decrease in amplitude.

In this type of simple harmonic motion, the restoring force is and the magnitude with how much the body experiences motion is proportional to each other when supplanted from its equilibrium position. The restoring force acting upon the object is simply the force used to stop the vibration.

Examples to better understand simple harmonic oscillators

Oscillating Pendulum: A pendulum is a mass suspended from a fixed, rigid support. When a push is given, the system experiences a vibration back and forth from its equilibrium position. This oscillation is periodic and goes by simple harmonic motion.

When a restoring force acts on the oscillations, it decreases as the amplitude decreases and ceases. This oscillation is known as simple harmonic motion.

Another example of the simple harmonic motion is the park swing that we notice in parks. These swings remain at rest until and force acts on them to start the movement. When a person sits on it and starts to swing, it starts the motion.

Swings, when given a slight push, displace from their equilibrium position and move back and forth. This motion is periodic, and also simple harmonic oscillations occur.

“Swings” by halfrain is licensed under CC BY-SA 2.0

Damped Harmonic Oscillator

Damping is the restriction of vibrations and oscillations in an equilibrium system by dissipation of energy. Damping oscillators are the ones in which vibrations decrease with time.

In a damping harmonic circuit, oscillations go on over a long period until and unless a restoring force is acted upon the equilibrium system. This restoring force is one of the reasons for the oscillation’s decay over time.

Damping harmonic oscillators are sub-divided into three types according to its damping factor.  The system is said to be critical damping when the damping factor is equal to one. When the damping factor is more than one, it is called overdamped or high damping. The system is said to be underdapmed if the damping factor is less than one.

The damping formula is connected to the Newton Second Law, and according to it, the formula goes like this for any damped harmonic oscillator.

C2 – 4mk = overdamped

C2 – 4mk = critically damped

C2 – 4mk = underdamped

The damping factor for a damping harmonic oscillator is that the vibrations return to zero at the shortest time interval. The system undergoes a harmonic motion; when a restoring force is applied, the oscillations eventually come to rest or back to the equilibrium position in less time interval.

The damped harmonic oscillation is one of the types of harmonic oscillator. An excellent example of damped oscillations is the weight suspended by spring. When the weight is suspended, it displaces from the equilibrium position back and forth and comes to rest eventually.

Harmonic oscillations are the reason for some systems to function with proper back and forth movements. We often tend not to notice the daily events occurring, but we see the harmonic oscillations in them.

Quantum Harmonic Oscillator

Quantum harmonic oscillator is analogical to conventional oscillators. Quantum harmonic oscillator is generally dealt with quantum mechanics. The built-in configuration of a quantum harmonic oscillator is different from the classical harmonic oscillator.

Since the built-in difference for both quantum harmonic oscillator and classic harmonic oscillator, there will be changes in the functionality of any system that comes under any of these oscillators.

Quantum harmonic oscillator models the vibrations in micro-level systems. For example, in quantum optics the representation of the behaviour of vibrations in molecules or molecular levels, wave packets is possible with quantum harmonic oscillators.

In this quantum harmonic oscillator the energy level is said to be evenly spaced without being a continuous one.

Differences in Quantum Harmonic Oscillator

The motion in the quantum harmonic oscillator is similar to the motion in classical harmonic oscillators with few differences. The oscillation or vibration in quantum harmonic oscillator is explained better using Schrodinger’s equation.

Quantum harmonic oscillator is analogical to conventional oscillators. Quantum harmonic oscillator is generally dealt with quantum mechanics. The built-in configuration of a quantum harmonic oscillator is different from the classical harmonic oscillator.

Since the built-in difference for both quantum harmonic oscillator and classic harmonic oscillator, there will be changes in the functionality of any system that comes under any of these oscillators.

Quantum harmonic oscillator models the vibrations in micro-level systems. For example, in quantum optics the representation of the behaviour of vibrations in molecules or molecular levels, wave packets is possible with quantum harmonic oscillators.

In this quantum harmonic oscillator the energy level is said to be evenly spaced without being a continuous one.

The motion in the quantum harmonic oscillator is similar to the motion in classical harmonic oscillators with few differences. The oscillation or vibration in quantum harmonic oscillator is explained better using Schrodinger’s equation.

Frequently Asked Questions

What is the use of harmonic oscillators?

Harmonic oscillators are used in a system to decay the oscillations in a system.

The harmonic oscillators in a system are periodic, and it decreases with the decrease in amplitude. The back and forth motion in a system goes on for a long time until a restoring force is applied to the system.

Why do we use a harmonic oscillator?

A harmonic oscillator is used so that the system comes to the equilibrium position in a concise span.

When the system is undergoing a motion, it will come to rest when a force is applied, and that force is known as restoring force. The oscillations in the system will come to rest or the equilibrium position with decreasing amplitude.

Mention the difference between simple harmonic motion and oscillations?

Simple harmonic motion is period, but oscillations vary.

In simple harmonic motion, the restoring force acting upon the system is not been mentioned. In oscillations, the force which helps decay the oscillations called as restoring force is generally not mentioned.

How is harmonic motion explained?

Harmonic motion is a periodic motion and is explained using a sine wave.

The oscillations of a vibrating system decay with decrease in amplitude. The oscillations undergo some change that is, they will face a restoring force or negative force. This force acts opposite to the motion in which system acts.

Hence, the restoring force and displacement of an oscillating body form the equilibrium position are proportional. One of the types of harmonic oscillator which is the damped harmonic oscillator and this is explained using Newton Second Law.

What is an electric oscillator?

An electric oscillator is the ones that produces electric signals in a circuit in which it is been fabricated and these signals are usually sine wave or square wave.

An excellent example of an electric oscillator is harmonic motion. This electric oscillator converts direct current into alternating current. It produces continuous waveforms without any input. Simple harmonic motion is one of the great examples of harmonic oscillations.

***********************

Scroll to Top