# Difference Between Free and Forced Oscillations

Throughout our daily lives, we encounter a variety of various body movements. Moving from one location to another in time is known as translator motion in the field of physics.

Consider a plane in the air, a train in motion, or a ball in motion; all of these are examples of translation motion. Then there's oscillatory motion, in which the same action is performed again by the body. The motion of a clock, a tuning fork, a swing, etc. are all instances of oscillatory motion. Several everyday occurrences may be explained by considering the role of oscillations and waves.

After an initial stimulation, if the system continues to oscillate under the influence of only its internal forces and not any external ones, we say that the oscillations are free. Yet, if the force from outside the system keeps the system in a state of oscillation, the vibrations are said to be forced.

The term "driving force" is used to describe the external force at work here. Hence, when a body oscillates without being affected by any external force, it is said to be executing free vibrations, but when a freely oscillating system is exposed to an external force, it begins creating forced vibrations (or oscillations). Let's compare and contrast free and forced oscillations and see what sets them apart.

## Free Oscillations

Consider a tuning fork as an illustration. A tuning fork has a predetermined frequency at which it will vibrate when hit. The tuning fork here is functioning as a free oscillator, and its vibrations at their natural frequency indicate that it is in free oscillation. So, a free oscillator is one that is allowed to oscillate at its own natural frequency without any interference from outside sources.

If, following an initial stimulation, the system oscillates the subject to its own internal forces without applying any external forces, then the vibrations are free. This state is known as "free oscillation" for the subject.

Without a driving force, a free oscillator will maintain a constant amplitude and period. In a perfect world, a free oscillator wouldn't be subject to damping unless some sort of resistance was given to its free oscillation.

## Forced Oscillations

Consider a swing as an illustration. With a single prod, the swing becomes a free oscillator, oscillating at its own natural frequency unaffected by any outside stimulus. But, it will ultimately stop swinging. But if you push the swing whenever it slows down or reaches a specific point, it behaves as a forced oscillator and continues to swing since it is being exposed to an external force. Hence, the subject gives in to the external force and oscillates at the same amplitude and frequency as the force. When this occurs, the resulting oscillations are known as forced oscillations.

Forced oscillations, in technical parlance, are those in which the body oscillates under the effect of a periodic force, but at a frequency other than its natural frequency.

## Differences: Free and Forced Oscillations

The following table highlights the major differences between Free and Forced Oscillations −

Characteristics

Free Oscillations

Forced Oscillations

Definition

Free oscillations are oscillations execute by a subject without being acted upon by an external force.They occur due to the elastic forces and inertia of the system.

Without any external force, the free oscillator is said to have constant amplitude and period.

Forced oscillations can be defined as the oscillations in which the body oscillates with a frequency other than its natural frequency under the influence of an external periodic force.

The external force here is called the driving force.

Example

Let’s take an example of a playground swing. When you push the swing just once, it oscillates at its own natural frequency without any interference from any external force, so it acts as a free oscillator.

Other examples of free oscillations include a tuning fork, a pendulum, etc.

Let’s take an example of a playground swing. When you push the swing each time it begins to slow down or reaches a certain point, it will continue to swing because it’s now being subjected to an external force, so it acts as a forced oscillator.

## Conclusion

Free and forced oscillations are two different types of oscillations that occur in different scenarios. Free oscillations occur when an object is set into motion without any external forces, and the motion continues without any external input. Forced oscillations occur when an external force is continuously applied to an object, causing it to vibrate at a specific frequency.

Understanding the difference between these two types of oscillations is important in various fields, including engineering, physics, and mechanics.

Updated on: 18-Apr-2023

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