Introduction
Every system, particle, and object oscillates at a natural frequency or collection of natural frequencies. The frequency at which an object tends to vibrate or oscillate without the application of external force is known as the natural frequency of the thing. All of these things and particles need an energy source that operates at a precise frequency between a few Hz and many MHz. An oscillator is a type of electrical device that can be used to meet this need. It is a signal-generating electrical circuit that is frequently used in computers, wireless receivers and transmitters, measurement systems, and other electronic systems of various types. It merely generates energy in the form of periodic electrical or mechanical vibrations.
Both sinusoidal and non-sinusoidal waveforms can be generated by an oscillator. In general, oscillators may be divided into two categories: sinusoidal oscillators and non-sinusoidal oscillators. We will solely discuss sinusoidal oscillators in this post. A sinusoidal oscillator is an oscillator that emits sine waves. They are categorised based on the elements that determine their frequency. Damped and undamped oscillations are two categories for the oscillations produced by sinusoidal oscillators. Damping describes the friction in an oscillating system. Let's examine the two vibrational kinds and highlight the significant differences between them.
It has been shown beyond doubt that everything oscillates, but only at its specific frequency. It is referred to as an object's frequency when it naturally moves, oscillates, or even vibrates. An object's frequency operates without the application of any external force. Each of these materials and things needs a certain amount of energy to shift their oscillation from a few HZs to a few MHz.
The primary distinction between damped and undamped vibration is that whereas in damped oscillations the amplitude of the waves produced tends to progressively decrease over time, in undamped oscillations it tends to remain constant and unchanging.
The mechanical phenomena of oscillations through an equilibrium point is referred to as vibration. This word's Latin origins translate to "shaking or brandishing." They might oscillate randomly or on a regular basis. Random oscillations are the movement of a tyre on a gravel road, whereas periodic oscillations are the motion of a pendulum. A tuning fork, a reed in a woodwind instrument or harp, a cell phone, etc. are examples of vibrations that are desired. However, there are also some unfavourable times, like as
Free vibration, forced vibration, and damped vibration are the three main categories of vibration. A mechanical system experiences a free vibration if it has been started in motion by an initial input that enables the system to vibrate freely. The time-varying disturbance that is imparted to mechanical systems is called forced vibration. Damped vibration, on the other hand, is the phenomena where a system's energy slowly vanishes due to friction and other resistances.
Damped vs Undamped Oscillations
The primary distinction between damped and undamped oscillations is that whereas in damped oscillations the amplitude of the waves being created continues to gradually decrease over time, it stays constant and unchanging in undamped oscillations. The oscillator provides the energy that is needed by the items. It is a tool for producing signals from different sources. It merely generates oscillations from a mechanical or electrical kind of energy on a regular basis.
Electrical oscillations that exhibit damping are those whose amplitude continually diminishes as a result of losses inherited in the power grid. In essence, it is a form of oscillation that gradually fades away. The energy generated in this way eventually decreases proportionately, and this decreases by an amount equal to the square of the previously computed amplitude. As a result, the oscillator's circuits are what create the damped oscillations.
The amplitude of the oscillations occurring at that period has stayed constant and unmodified if the losses that have occurred in the electrical system can be compensated for.Undamped oscillations are this type of oscillation. The oscillations that remain constant throughout time are known as undamped oscillations, to put it another way.
Difference Between Damped and Undamped Oscillation in Tabular Form
| Parameters of comparison | Damped Oscillations | Undamped Oscillations |
| Meaning | the oscillations whose amplitude continuously decreases with time. | The kind of oscillation in which the amplitude remains constant throughout time. |
| Power Losses | As they continue to decrease, these oscillations do not last for an extended period of time.. | This type of oscillation has no power losses |
| Frequency | The frequency doesn't change. | Over time, the amplitude remains constant. |
| Period | Eventually, the damped oscillation stops | . The ones that are undamped don't change. |
| Example | As the pendulum swings, the vibration progressively becomes less intense and eventually ceases. | A toy or spring horse for children. |
What are Damped Oscillations?
Damped oscillations are electronic oscillations whose amplitude continuously decreases over time as a result of losses present in the electrical system where the oscillations are produced. It alludes to an oscillation that eventually stops. An oscillator is constantly susceptible to factors that cause some of the oscillator energy to dissipate as heat or in other ways. Since energy is inversely proportional to amplitude, the amplitude steadily drops until the oscillator reaches equilibrium. The damped oscillations are then generated by the oscillator circuits. The oscillation frequency, however, is unaffected because it is a function of the circuit characteristics. The swinging pendulum, whose vibration gradually decreases and eventually ceases, is the greatest illustration of a damped oscillation.
Damped oscillations are oscillations whose amplitude continually decreases as a result of losses inherited in the electrical system of power. In essence, it is a form of oscillation that gradually fades away. As a result, the energy generated steadily decreases its proportopnate, which is equal to the amplitude squared. As a result, the oscillator's circuits are what create the damped oscillations.
The oscillation's frequency doesn't vary. This is thus because the characteristics of the circuit affect frequency. An illustration of a pendulum that gradually slows down and eventually stops moving might help explain the idea of damped oscillation. Therefore, it may be claimed that motion is dampened and consequently, oscillation is dampened everywhere there is a loss of energy.
The progressive reduction in oscillation amplitude that results from the dissipation of the stored energy is what dampens an oscillation. Most oscillations in typical circumstances have amplitudes that are either more or less damped, therefore it is necessary to make up for the energy.
What are Undamped Oscillations?
If the electrical system's losses could be made up for, the oscillation's amplitude would stay constant and, as a result, would be impervious to both external disturbances and changes in the beginning circumstances. Undamped oscillation is the name given to this sort of oscillation. Simply described, undamped oscillations are oscillations whose amplitude does not change over time. Systems that are capable of producing these oscillations are known as self-excited oscillating systems, and in a non-linear dissipative system, they are sustained by an external energy source. There won't be any power losses or mechanisms to make up for them if the oscillator generates undamped vibrations.
When the losses that have occurred in the electrical system can be made up for, undamped oscillations are created. As a result, the amplitude of the oscillations occurring at that moment remains constant and unaltered. The oscillations that remain unaltered throughout time are known as the undamped oscillations, to put it another way.
The essential characteristic of undamped oscillations is the absence of power losses when an oscillator produces them. In contrast to damped oscillations, if the oscillations being generated are undamped, there won't be any power loss, necessitating no need to make up for the energy or other losses it may have caused. Because of the power loss in the damped oscillations, the majority of the energy needs to be compensated.
Difference between Damped and Undamped Oscillations in Points
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Damped and undamped oscillations' definition
Damped and undamped oscillations are two categories for the oscillations produced by sinusoidal oscillators. Damped oscillations are electronic oscillations whose amplitude continuously decreases over time as a result of losses present in the electrical system where the oscillations are produced. However, if the electrical system's losses could be made up for, the oscillation's amplitude would stay constant and, as a result, would be impervious to both external disturbances and changes in the beginning circumstances. Undamped oscillation is the name given to this sort of oscillation.
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Damped vs. Undamped Oscillations: Energy Loss
Since the power loss is not compensated for in damped oscillations, the produced wave's amplitude steadily diminishes over time. Such oscillations eventually stop since they cannot last for an extended period of time. The motion becomes dampened when energy is lost. On the other hand, if the oscillator circuit generates undamped oscillations, neither power losses nor a means of making up for them exist. They oscillate with constant amplitude, which means that there is no energy loss because the amplitude does not decrease with time.
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Cause
In an oscillatory system, damping is the gradual reduction in oscillation amplitude brought on by the dissipation of stored energy. The friction caused by the fluid travelling through the tube causes damping, which tends to put a stop to oscillations and reduce the transducer system's frequency response. All sorts of vibrations are typically more or less dampened, therefore in order to make the oscillations undamped, it is required to make up for the energy losses by giving extra energy from a different source. Any energy that is brought in from the outside must be in phase with the established oscillations.
- The primary distinction between damped and undamped oscillations is that, in damped oscillations, the generated wave's amplitude progressively drops over time, but in the case of undamped oscillations, the generated wave's amplitude does not vary over time. The motion becomes dampened when energy is lost. On the other hand, if the oscillator circuit generates undamped oscillations, neither power losses nor a means of making up for them exist. In an oscillatory system, damping is the gradual reduction in oscillation amplitude brought on by the dissipation of stored energy. Since most vibrations of all kinds are somewhat dampened, it is required to make up for the energy lost by adding more energy from a different source in order to make the oscillations undamped.
- The major distinction between damped and undamped oscillations is that the former are oscillations whose amplitude continuously decreases with time, whilst the latter are oscillations whose amplitude remains constant and unchanging throughout time.
- These oscillations don't last for very long and eventually come to an end since the amplitude produced by the waves in damped ones steadily decreases. The oscillation creates an undamped oscillation even if there is no power loss.
- While the amplitude of an undamped oscillation doesn't fluctuate over time, the frequency of a damped oscillation stays constant.
- The undamped oscillations persist long after the damped ones have died.
- A pendulum that swings steadily, then progressively slows down and stops after some time is an illustration of a damped oscillation. A child's spring horse or a toy is an illustration of undamped oscillation.
Conclusion
It has been determined that both damped and undamped oscillations offer advantages and disadvantages. It is referred to as an object's frequency when it naturally moves, oscillates, or even vibrates. An object's frequency operates without the application of any external force. Each of these materials and things needs a certain amount of energy to shift their oscillation from a few HZs to a few MHz.
A sinusoidal wave and a non-sinusoidal wave can both be produced by an oscillator, which is often used to create oscillations. There are two types of oscillators: oscillators with sinusoidal waveforms and oscillators with non-sinusoidal waveforms. The oscillator provides the energy that is needed by the items. It is a tool for producing signals from different sources. It merely generates oscillations from a mechanical or electrical kind of energy on a regular basis.
References
- https://journals.aps.org/prb/abstract/10.1103/PhysRevB.66.184201
- https://ui.adsabs.harvard.edu/abs/1981oxny.book…..H/abstract
- https://pubs.acs.org/doi/pdf/10.1021/ja01453a010
