We have previously discussed periodic motion in this blog. Oscillatory motion or vibratory motion is special kind of periodic motion. **Please note that the term oscillation is wrongly used in place of periodic motion. You, after reading this blog should avoid this mistake**. Oscillation is special kind of periodic motion. **All oscillations are periodic motion but all periodic motions are not oscillations.**

## What is Oscillatory Motion?

**When the body is** **at equilibrium position no net external force acts on it.** Therefore, if it is left there at rest, it remains there forever. If we externally displace the body from the position, a force comes into play which tries to bring the body back to the equilibrium point. As a result, giving rise to **oscillations or vibrations**. For example, a ball placed in a bowl will be in equilibrium at the bottom. If displaced a little from the point, it will perform oscillations in the bowl. Every oscillatory motion is periodic, but every periodic motion need not be oscillatory. Uniform circular motion is a periodic motion, but it is not oscillatory.

## Definition of Oscillatory Motion

**To and fro motion of an object from its mean/equilibrium position is called as oscillatory motion.** The motion on either side of equilibrium position should be same. In the ideal condition the object can be in oscillatory motion forever in the absence of friction. But, in the real world, it settle down in equilibrium via damping. Hence, the name damped oscillation.

## Displacement from mean position

Any periodic function can be expressed as a superposition of sine and cosine functions of different time periods with suitable coefficients.

The displacement can be represented by a mathematical function of time. In case of periodic motion, this function is periodic in time. One of the simplest periodic functions is given by

f(t) = A cos(ωt)

ω is angular frequency.

f(t) is displacement from mean position.

A is amplitude.

## Time Period and Frequency of Oscillatory Motion

We know that periodic motion repeats itself after regular intervals of time. **Time period is the smallest interval of time after which the motion repeats.** You can call **time period** as simply **period**. We use English letter **T** to represent time period.

**The number of times motion repeats in a second is called frequency**. It is represented by Greek letter **ν**.

Thus, Mathematically **ν = 1/T**.

**ω/2π gives frequency.**

**Time Period = 2π/ω**

## Examples of Oscillatory Motion

Following are the examples of oscillatory motion:

- Vibrating strings of musical instruments is a mechanical example of oscillatory motion
- Oscillation of simple pendulum
- Alternating current is an electrical example of oscillatory motion

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