What Is The Amplitude Of Oscillation: You Should Know


The amplitude of oscillation explains the maximum or highest displacement of the oscillating body. The article discusses exhaustively about what is the amplitude of oscillation and how to calculate it.

Amplitude is the quantity of the oscillating body like angular frequency and time period. The quantity measures the maximum displacement of the body on both sides of its mean position. That means it shows us how much the oscillating body deviates from its mean position during oscillation.

Oscillation involves the to and fro movement of the body from its equilibrium or mean position. Every oscillation has three main characteristics: frequency, time period, and amplitude. Out of which, we already discussed concepts of the frequency and time period in the previous articles. 

Let’s start a discussion about the amplitude of oscillation or oscillation amplitude by taking the example of a simple pendulum. The pendulum swings angularly through its mean position towards the highest distance away from its mean position. The maximum or highest distance of the oscillating body away from its center or mean position is termed its maximum displacement. In contrast, the magnitude of maximum displacement of the oscillation body on both sides of the mean position is called its amplitude of oscillation

What is the Amplitude Of Oscillation?
What is the Amplitude Of Oscillation?
How to calculate Oscillation Amplitude?
How to calculate Oscillation Amplitude?

From the sinusoidal graph, we noted that the oscillation amplitude is the distance between a crest, trough, and mean position

Therefore, the oscillation amplitude or the magnitude of maximum displacement x is given by sin wave equation as,

[latex]x = Asin(\omega t+\phi )[/latex] …………(*)

Where A is the amplitude of oscillation.

 [latex]\omega[/latex] is the angular velocity.

[latex]\phi[/latex] is the phase shift.

We will discuss how to calculate the oscillation amplitude equation (*) from the sinusoidal graph in the later part.  

Since every wave has an amplitude, the peaks in the graph show that the amplitude explains the degree or level of intensity variation in various waves such as the sound waves. Therefore, it is also interpreted as the loudness of the sound. 

 Amplitude in Sound Waves
What is the Amplitude Of Oscillation?
Sound Waves

In the graph, we noted that the difference between the highest amplitude peak or positive value and the lowest amplitude peak or negative value is called the ‘peak-to-peak amplitude’ of the oscillating body.

Read more about Angular Frequency Simple Harmonic Motion

How to find Oscillation Amplitude of from Graph? 

We can obtain the oscillation amplitude from the graph of the sinusoidal function of the oscillating body.  

The amplitude of oscillation is defined when we sketch the graph of the oscillating variables, such as a displacement against time. The peaks in the sinusoidal graph are the amplitude of oscillation which describes – how much distance the body oscillates from the mean position on either side. 

Within any oscillation system, the magnitude of variation in the oscillation variable of the body with each oscillation is termed oscillation amplitude. In most cases, the oscillating variable is displacement. When we plot the graph of the sinusoidal function, with an oscillation variable displacement as the vertical axis and the time as the horizontal axis, the vertical distance between the mean value to the extrema of the curve illustrates the oscillation amplitude.

How to find Amplitude of oscillation from graph?
How to calculate Oscillation Amplitude?
(credit: shutterstock)

In the sinusoidal function graph, the x-axis is considered as the mean position of the oscillation body. Therefore, whatever may be the body’s starting position, the displacement is measured from its mean position. Since the graph is a sine function – which illustrates periodic phenomena, the peaks in the graph display the quantities of the oscillating body, such as a period and amplitude. 

How to find the Amplitude?
How to calculate Oscillation Amplitude
form graph?

From the peaks, the amplitude of oscillation is calculated as one-half of its difference between maximum and minimum values.  

[latex]amplitude = \frac{1}{2}\mid max -min \mid[/latex]

Therefore, the magnitude of oscillation amplitude is always positive. 

We can also find the oscillation amplitude and time period from the generalized equation of the sine graph as follows: 

y=A⋅sin(B(x+C))+D

where we can find the quantities of oscillation body as follows:

Oscillation Amplitude: A

Time Period: [latex]\frac{2\pi }{B}[/latex]

Phase Shift – how far the body moves horizontally from mean position: C.

Vertical Shift – how far the body moves vertically from mean position: D.

How to calculate Oscillation Amplitude?
How to calculate Oscillation Amplitude?
Sine Wave Function Graph (credit: mathsisfun)

Read more about Angular Equation of Motion.

What is the Amplitude and Frequency of Oscillation?

The amplitude and frequency are quantities of oscillation bodies that define the rate of oscillation. 

The body oscillates when it moves from its mean position to the highest position and returns to its mean position. Here, the amplitude represents the maximum displacement of the body from its mean position. Whereas the frequency represents how much the body oscillated from its mean position. 

What is the Amplitude and Frequency Of Oscillation?

Depending on amplitude and frequency, the oscillation is classified into the following three types: 

Damped Oscillation

Suppose the body oscillates with the decreasing amplitude because of the presence of air resistance force and at one point of time and it comes to rest since its body’s both quantities dissipated. In that case, it is called “damped oscillation”

Free Oscillation 

Suppose the body oscillates freely with a constant amplitude and definite frequency because of the absence of frictional force. In that case, it is called “free oscillation”, and its frequency is called the ‘natural frequency’ of the oscillating body. 

Forced Oscillation

It is also called the oscillation of a stretched string or swing. Suppose the body oscillates with the decreasing amplitude because of the mechanical energy of the swing, and it comes to rest since its both quantities dissipated. In that case, it is called ‘forced oscillation’.

Let’s take the example of the suspended paddle ball that is tied to your hand.

 Amplitude and Frequency of Oscillation
Amplitude and Frequency of Oscillation
(credit: lumenlearning)

Case 1:

If you keep your hand stable, the ball bounces up and down, including a certain amount of damping (i.e., air drag force applied).

Case 2:

Increasing the ball’s frequency by moving your hand up and down, the ball also responds with increasing amplitude. If you drive the ball with a frequency equal to its natural frequency, its amplitude rises per oscillation. The event of driving the body with a frequency equivalent to the natural frequency is called resonance. Whereas the body performed at its natural or fundamental frequency is said to resonate.

Case 3:

if you furthermore increase its frequency higher than its natural frequency, its amplitude starts decreasing until the oscillations almost disappear. So your hand movement no longer affects the ball. 


Manish Naik

Hello, I'm Manish Naik completed my MSc Physics with Solid-State Electronics as a specialization. I have three years of experience in Article Writing on Physics subject. Writing, which aimed to provide accurate information to all readers, from beginners and experts. In my leisure time, I love to spend my time in nature or visiting historical places. I am honoured to be part of LambdaGeeks. Looking forward to connecting you through LinkedIn - https://www.linkedin.com/in/manish-ashok-naik/ Also, for Maharashtra travel guide and heritage conservation articles, visit my website Wandering Maharashtra - https://wanderingmaharashtra.com/travel-blogs/

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