The **key difference between damped oscillation and forced oscillation** is that damped oscillation is the reduction in amplitude of an oscillator, whereas forced oscillation is the oscillation that happens when an oscillating system is driven by a periodic force that is external to the oscillating system.

Oscillation is the back-and-forth movement in a regular rhythm. There are two major types of oscillation as damped oscillation and forced oscillation. Damped oscillation refers to oscillation that degrades over a specific period of time. Forced oscillation, on the other hand, refers to oscillation that takes place due to the effect of an external periodic force.

### CONTENTS

1. Overview and Key Difference

2. What is Damped Oscillation

3. What is Forced Oscillation

4. Damped Oscillation vs Forced Oscillation in Tabular Form

5. Summary – Damped Oscillation vs Forced Oscillation

## What is Damped Oscillation?

Damped oscillation is the type of oscillation that takes place through the reduction of the amplitude of an oscillator. In a system having this type of oscillation, the amplitude of the oscillation gradually decreases with time. In fact, the term damping refers to this the reduction of amplitude. We can define damped oscillation simply as the oscillation that degrades over a specific time period of time. Some common examples of this type of oscillation include a weight on a spring, a swinging pendulum, and an RLC circuit.

Moreover, upon subjecting a damped oscillator to a damping force, (force has to be linearly dependent upon the velocity similar to the viscous damping), the oscillation tends to have exponential decay terms that tend to depend on a damping coefficient. We can express the damping force as follows:

Where F is the damping force, c is a coefficient of variation, and v is the velocity. Therefore, we can express the damping coefficient as follows:

Here, m is the mass of the oscillator. This means the damping force is proportional to c but inversely proportional to the mass of the oscillator.

## What is Forced Oscillation?

Forced oscillation can be described as a type of oscillation that occurs when an oscillating system is driven by a periodic force that occurs external to the oscillating system. In contrast, free oscillations occur when the body oscillates with its own frequency. The body that undergoes forced oscillation tends to oscillate with the frequency of the periodic force.

A common example is when a child is using his feet to move the swing or when someone else pushes the swing to maintain the movement. Moreover, resonance can be given as a particular case of forced oscillation.

## What is the Difference Between Damped Oscillation and Forced Oscillation?

Damped oscillation and forced oscillation are two types of oscillations. The key difference between damped oscillation and forced oscillation is that damped oscillation is the reduction in amplitude of an oscillator, whereas forced oscillation is the oscillation that happens when an oscillating system is driven by a periodic force that is external to the oscillating system.

Below is a summary of the difference between damped oscillation and forced oscillation in tabular form for side by side comparison.

## Summary – Damped Oscillation vs Forced Oscillation

Damped oscillation refers to oscillation that degrades over a specific period of time while forced oscillation refers to oscillation that takes place due to the effect of an external periodic force. The key difference between damped oscillation and forced oscillation is that damped oscillation is the reduction in amplitude of an oscillator, whereas forced oscillation is the oscillation that happens when an oscillating system is driven by a periodic force that is external to the oscillating system.

##### Reference:

1. “Damped Oscillations.” *Physics LibreTexts*.

2. “Forced Oscillations.” *Physics LibreTexts*.

##### Image Courtesy:

1. “Animated-mass-spring-faster” By Svjo – (CC BY-SA 3.0) via Commons Wikimedia

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