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gravity force simulation screenshot

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# INTRODUCTION

Interference is a process in which two waves merge by adding their displacements at every point in space and time, resulting in a consequent wave of larger, lower, or equal amplitude.

![wave](//images.ctfassets.net/4yflszkpcwkt/z9qoV8ycEbzws0KKyl7RH/86b77ba60f4f421a9c99cd7206c7be88/1200px-Interference_of_two_waves.svg.png)
[Source](https://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Interference_of_two_waves.svg/1200px-Interference_of_two_waves.svg.png) 

## DEFINITION

When waves collide at the same time as touring throughout the identical medium, that is called wave interference. The medium takes on a form due to the internet impact of the 2 awesome waves at the medium’s debris because of wave interference.

## WAVE INTERFERENCE TYPES

There are two types of Wave interference –

### CONSTRUCTIVE INTERFERENCE

- Constructive interference is a form of interference that occurs when two interference waves have the same displacement in the same direction at any point along with the medium. 
- In this scenario, both waves have upshifts, so the medium has a larger upshift than the shifts of the two interfering pulses. 
- Constructive interference is detected at any point where the two interference waves shift upwards. 
- However, if both opposite waves are shifted down, you will be notified.

### DESTRUCTIVE INTERFERENCE 

Destructive interference occurs when two interference waves are displaced in opposite directions at any point along with the medium. 

![interfera](//images.ctfassets.net/4yflszkpcwkt/1REsmOudgjgOAypKF0JJ1X/66dec13709b58f47009765d4b817e1eb/constructiveanddestructiveinterference.png)
[Source](https://www.physics-and-radio-electronics.com/physics/images/constructiveanddestructiveinterference.png) 

## PRINCIPLE OF SUPERPOSITION

If two or more waves of the same type collide at the same point, the resulting amplitude at that point is equal to the vector sum of the amplitudes of the individual waves, according to the wave superposition principle.

## APPLICATIONS OF INTERFERENCE OF WAVES IN REAL LIFE
* Soap bubbles are another real-life example of light interference.
* Wet roads with color patches during the rainy season, color patches on the roads are plainly seen.
* Anti-reflective coating 
* Oil on the water's surface
* Hologram.

# SUMMARY
- The medium takes shape as a result of the net influence of the two separate waves when waves collide.
- The resulting amplitude is the sum of the individual amplitudes when one wave crest meets another wave crest with the same frequency at the same point. This is called constructive interference. 
- When one wave crest collides with another wave valley, the combined amplitude is the difference between the individual amplitudes-this is known as destructive interference.

## FAQs

**Q. State the interference definition.**

Interference is a process in which two waves merge by adding their displacements at every point in space and time, resulting in a consequent wave of larger, lower, or equal amplitude.

**Q. What are the types of interference?**

There are two types of interference:
1. Constructive interference
2. Destructive interference

**Q. State true or false: The interference of waves results in the medium taking shape resulting from the net effect of the two individual waves.**

True, the medium takes shape as a result of the net influence of the two separate waves when waves collide.

**Q. State the principle of superposition of waves?**

According to the superposition principle, when two or more waves merge in space, the resulting disruption is equivalent to the algebraic total of the individual disturbances.

_We hope you enjoyed studying this lesson and learned something cool about **Wave Interference**! Join our Discord community to get any questions you may have answered and to engage with other students just like you! We promise, it makes studying much more fun!😎_

## REFERENCE 
1. Interference of Waves: [https://byjus.com/physics/interference-of-waves/](https://byjus.com/physics/interference-of-waves/)** **Accessed 19th April 2022.
2. Interference of Waves: [https://www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves#:~:text=Wave%20interference%20is%20the%20phenomenon,the%20particles%20of%20the%20medium](https://www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves#:~:text=Wave%20interference%20is%20the%20phenomenon,the%20particles%20of%20the%20medium). Accessed 19th April 2022.
3. Wave Interference: [https://en.wikipedia.org/wiki/Wave_interference](https://en.wikipedia.org/wiki/Wave_interference) Accessed 19th April 2022.

The latest wave with high, small, or equal amplitude is created by combining waves.


Wave Interference Study Guide

# INTRODUCTION

The distance a wave travels in a particular amount of time, such as the number of meters a wave travels per second, is called the velocity of the wave.

Plucking a guitar string is an example of wave speed.

If someone plucks a guitar string, the strings appear to move in a transverse wave pattern. Although the sound wave is a longitudinal wave, the wave on the guitar is transverse. The particles in the string travel perpendicular to the wave's propagation direction.

## WAVE SPEED FORMULA

![speed](//images.ctfassets.net/4yflszkpcwkt/K9juX6FTehs3irY44QAy6/9a47cc16d04210dce1786915740519b7/822003748.png)
[Source](http://thepropertiesofwaves.weebly.com/uploads/2/6/2/5/26255225/822003748.png) 

Wave speed equation (Speed = Wavelength x Frequency) relates wave speed to wavelength and frequency. When the wavelength and frequency are known, this equation can be used to calculate wave speed.

Wave frequency is the number of waves that move per second. In addition, the duration is calculated as the reciprocal of the frequency of the wave. Wave wavelength is the distance between the corresponding points of two consecutive waves.

## VARIABLES AFFECTING WAVE SPEED

* Wavelength
* Speed
* Distance
* Frequency

The above given four variables are affecting wave speed.

## THE MEDIUM'S DEPENDENCE

- The speed of most waves depends on the medium through which the wave travels. 
- Waves generally pass through solids fastest and gas slowest. 
- This is because the particles are closest to each other in a solid, while the particles are the closest to each other in a gas. 
- If the particles are further apart, the energy distribution will take longer to pass through the medium from one particle to another.

## WAVE SPEED EXAMPLE

![speed](//images.ctfassets.net/4yflszkpcwkt/5ygQlyq43Lr9rw6xxynYQo/89fd2db79d3868195c4ee1cdfb9a9d13/v4-460px-Calculate-Wavelength-Step-4-Version-3.jpg)
[source](https://www.wikihow.com/images/thumb/a/a0/Calculate-Wavelength-Step-4-Version-3.jpg/v4-460px-Calculate-Wavelength-Step-4-Version-3.jpg) 

## SUMMARY

- Wave speed equation (Speed = Wavelength x Frequency) relates wave speed to wavelength and frequency. 
- When the wavelength and frequency are known, this equation can be used to calculate wave speed.
- 
- The frequency of a wave is the number of waves that move in one second. 
- In addition, the time period is calculated as the reciprocal of the wave frequency. 
- The wavelength of a wave is the distance between any two consecutive waves' corresponding points.

## FAQs

**Q. What is wave speed?**

The distance traveled by a given point (e.g., the summit) of a wave at a given time interval is the velocity in the case of a wave.

**Q. What is the speed of a wave that has a wavelength of 2 m and a frequency of 1.5 Hz?**

Speed = Wavelength x Frequency

Speed = 2 x 1.5 

Speed = 3 m/sec.

**Q. Sound energy travels through matter in waves. Do sound waves travel faster through air or water? Explain your answer.**

Liquids are not as densely packed. Gasses, on the other hand, are relatively loosely packed. This allows sound to travel much more quickly through a solid than through a gas. In water, sound travels four times quicker and farther than it does in air.

**Q. What is the formula for the speed of a wave?**

Wave Speed = Wavelength x Frequency

_We hope you enjoyed studying this lesson and learned something cool about **Wave Speed**! Join our Discord community to get any questions you may have answered and to engage with other students just like you! We promise, it makes studying much more fun!😎_

## REFERENCE 
1. Wave Speed: [https://byjus.com/physics/wave-speed/](https://byjus.com/physics/wave-speed/) Accessed 19th April 2022.
2. The Speed of Wave: [https://www.physicsclassroom.com/class/waves/Lesson-2/The-Speed-of-a-Wave#:~:text=If%20the%20crest%20of%20an,wave%20is%202.5%20m%2Fs](https://www.physicsclassroom.com/class/waves/Lesson-2/The-Speed-of-a-Wave#:~:text=If%20the%20crest%20of%20an,wave%20is%202.5%20m%2Fs). Accessed 19th April 2022.
3. Wave Speed Formula: [https://www.toppr.com/guides/physics-formulas/wave-speed-formula/](https://www.toppr.com/guides/physics-formulas/wave-speed-formula/) Accessed 19th April 2022.
4. Real-life Examples of Transverse Waves: [https://studiousguy.com/real-life-examples-of-transverse-wave/](https://studiousguy.com/real-life-examples-of-transverse-wave/) Accessed 19th April 2022.

The distance traveled by a wave in a particular length of time is referred to as wave speed.


Wave Speed Study Guide

# INTRODUCTION

Longitudinal and transverse waves are 2 types of mechanical waves. Examples of longitudinal waves include sound waves, seismic P-waves, and ultrasonic waves. Electromagnetic waves and ocean waves are examples of shear waves. Refraction and compression form longitudinal waves.

![wavs](//images.ctfassets.net/4yflszkpcwkt/6SuzuqNZ2Ydokz6gX5LOU7/5c0444aa5c06478102e0cb069074364f/maxresdefault.jpg)
[Source](https://i.ytimg.com/vi/AVM7fKjurp4/maxresdefault.jpg) 

## FORMULA FOR LONGITUDINAL WAVES

**Y(x,t) = y<sub>0</sub>cos[ω (t – x  / c)]**

* Where y is the displacement of the point on the propagating sound wave and x is the distance traveled from the source of the wave.
* t is the elapsed time. 
* The amplitude of the vibration is given by y<sub>0</sub>.
* The velocity of the wave is given by c.
* ω is the angular frequency (in degrees) of the wave. 
* Time = quantity x / c (waves take to travel   distance x). 
* The formula for wave frequency (f) is f = ω2π

## LONGITUDINAL WAVE DIAGRAM

![wave](//images.ctfassets.net/4yflszkpcwkt/3bs4ZF8tOc869x4VffZDMW/36198b8d4edbcce63db8641799ce7e05/image-56.png)
[Source](https://www.shalom-education.com/wp-content/uploads/2021/03/image-56.png)

## CHARACTERISTICS OF LONGITUDINAL WAVES
* Wavelength is the distance between two adjacent peaks or any two identical locations.
* The distance between the wave's midpoint and its peak or between the wave's midpoint and its dip.
* The number of full waves that pass by a specific place each second is known as frequency. Hertz is the unit of frequency measurement (Hz).
* Compression refers to the part of the longitudinal wave particles that are closest to each other. 
* For longitudinal waves, the particles become thinner when they are farthest apart.

## DIFFERENCES BETWEEN TRANSVERSE AND LONGITUDINAL WAVE

### LONGITUDINAL WAVE
* The medium moves in the same direction as the shaft. 
* There is only one action dimension. 
* Waves cannot be polarized or aligned.

### TRANSVERSE WAVE
* The medium is traveling in the opposite direction of the wave.
* It has two-dimensional effects.
* The wave might be aligned or polarized.

# SUMMARY
- Longitudinal and transverse waves are 2 types of mechanical waves. 
- Examples of longitudinal waves include sound waves, seismic P-waves, and ultrasonic waves.  
- Refraction and compression form longitudinal waves. 

## FAQ’s

**Q. What can a longitudinal wave pass through?**

Through a gas, a longitudinal wave can travel.

**Q. Do longitudinal waves need air?**

Yes, longitudinal waves need air.

**Q. What is the distance between waves?**

The wave height is the vertical distance between the crest and the trough. The wavelength is the horizontal distance between two adjacent crests or troughs.

**Q. What is the velocity of a longitudinal wave?**

Longitudinal waves, such as sound, travel through a medium at different speeds depending on their density and elasticity. In the air, sound travels at 0.33 kilometers per second (0.2 miles per second), 1.5 kilometers per second in water, and 5 kilometers per second in steel.

**Q. Are electromagnetic waves longitudinal or transverse?**

Electromagnetic waves are transverse waves.

**Q. Why is a sound wave called a longitudinal wave?**

Because the particles of the medium through which the sound is transmitted vibrate parallel to the direction in which the sound wave moves, sound waves in air (and any fluid media) are longitudinal waves.

_We hope you enjoyed studying this lesson and learned something cool about **Longitudinal Waves**! Join our Discord community to get any questions you may have answered and to engage with other students just like you! We promise, it makes studying much more fun!😎_

## REFERENCE 
1. Longitudinal Wave: [https://byjus.com/physics/longitudinal-waves/](https://byjus.com/physics/longitudinal-waves/) Accessed 19th April 2022
2. Longitudinal Wave: [https://byjus.com/physics/longitudinal-waves/](https://byjus.com/physics/longitudinal-waves/) Accessed 19th April 2022
3. What are Waves? [https://www.shalom-education.com/courses/ks3-physics/lessons/waves/topic/what-are-waves/](https://www.shalom-education.com/courses/ks3-physics/lessons/waves/topic/what-are-waves/) Accessed 19th April 2022

Longitudinal waves form when the substance is moved in almost the same way as the wave propagates.

 Longitudinal Waves Study Guide

# INTRODUCTION 

![PENDULUM](//images.ctfassets.net/4yflszkpcwkt/ra6NQ49Bavm9XXO68H73G/2bd849dec237800bcb8b66aff0d18e43/pendulum_custom-40c376ae65462f2f44e1a84a115e90e768a235d1-s800-c85.webp)
[Source](https://media.npr.org/assets/img/2011/05/16/pendulum_custom-40c376ae65462f2f44e1a84a115e90e768a235d1-s800-c85.webp)

We see oscillatory and periodic motion all around us. A swing in the park moves to and fro; the hands of a clock go around every day; the strings on a guitar vibrate to produce sounds. Yet, all of these motions share commonalities and differences. 

In physics, the study of oscillatory motion is important everywhere, from the orbits of planets to the vibration of atoms and molecules. One such oscillatory motion which has a lot of practical uses is the simple harmonic motion (SHM). What makes SHM different from other types of oscillatory motion? Let’s find out!  

## OSCILLATORY AND PERIODIC MOTION

Before getting to SHM, it is important to understand oscillatory and periodic motion. 

**Oscillatory Motion**

- An oscillatory motion is the to and from motion executed by an object about a mean point. 
- A simple example is the motion of a pendulum about its mean position. 
- A weight hanging at the end of a long thread moves to and fro until it comes to a stop at the mean or ‘equilibrium’ position. 
- At the mean position, the pendulum has maximum velocity, and at the extreme position, a restoring force pulls it back. 

**Periodic Motion**

![CLOCK](//images.ctfassets.net/4yflszkpcwkt/3d2z3b39tjyt3nc2AdPX7G/bd1b6f8cd4df2a2025d8351a03bb09eb/Periodic-Motion.jpg)
[Source](https://qsstudy.com/wp-content/uploads/2017/02/Periodic-Motion.jpg)

- A periodic motion is a type of motion that repeats itself over a period of time. 
- The movement of the hands of a clock exhibits periodic motion. 
- From the example, we can see that not all periodic motion is oscillatory. 
- However, the motion of a pendulum is both oscillatory and periodic. 

## THE SIMPLE HARMONIC MOTION 

- An oscillatory motion becomes simple harmonic when the acceleration of the particle is directly proportional to its displacement from the mean position. 
- From this, we can see that all SHM are oscillatory in nature, but not all oscillatory motion is simple harmonic. 
- In fact, SHM can be called a special case of oscillatory motion. 

![HARM](//images.ctfassets.net/4yflszkpcwkt/4SSrsuCa6zXY7zzyq5QPNP/ca0736e50980cc8ed97235e4dc057a0a/SHM4-660x327.JPG)
[Source](https://media.geeksforgeeks.org/wp-content/uploads/20210624231653/SHM4-660x327.JPG)

- A simple example of an SHM is the spring-mass system shown in the diagram above. 
- When the mass which rests on a frictionless surface is extended, the spring exerts a restoring force equal to the magnitude of the extension. 
- The force generated by the spring is given by the formula: 

__F = -kx__

K is the spring constant measured in N/m

X is the displacement of the mean position

The negative sign indicates that the force acts in the opposite direction of motion

## SOME SIMPLE HARMONIC MOTION EXAMPLES  
* A simple pendulum 
* Vibrating springs
* The motion of a torsion pendulum 
* The vibration of atoms inside the atomic lattice 
* Liquid oscillating in a U-tube
* Rolling a marble over a concave surface

# SUMMARY
* An oscillatory motion is the to and from motion executed by an object about a mean point.
* A periodic motion is a type of motion that repeats itself over a regular time interval.
* In a simple harmonic motion, the acceleration of the particle is directly proportional to its displacement from the mean position.

## FAQs

**Q. What is unique about simple harmonic motion?**

An SHM is a special type of oscillatory motion that is also periodic. The restoring force in an SHM is directly proportional to the displacement of the object from the mean position.                                    

**Q. What change can be made to increase the period of the oscillation if spring is attached to a mass and oscillates freely in simple harmonic motion?**

Considering the characteristics of simple harmonic motion, to increase the period of oscillation, the spring stiffness needs to be reduced, and the mass needs to be increased. 

**Q. What is the importance of simple harmonic motion?**

Simple harmonic motion finds application in all fields, starting from the design of circuits to the study of gravitational waves. 

**Q. What is the maximum displacement of a body in simple harmonic motion?**

The maximum displacement of a body in SHM is called its amplitude. 

_We hope you enjoyed studying this lesson and learned something cool about **Simple Harmonic Motion**! Join our Discord community to get any questions you may have answered and to engage with other students just like you! We promise, it makes studying much more fun!😎_

## SOURCES 
1. Simple Harmonic Motion:  [https://byjus.com/jee/simple-harmonic-motion-shm/](https://byjus.com/jee/simple-harmonic-motion-shm/) Accessed 13th April 2022.
2. Simple Harmonic Motion: [https://www.geeksforgeeks.org/simple-harmonic-motion/](https://www.geeksforgeeks.org/simple-harmonic-motion/)Accessed 13th April 2022. 
3. Simple Harmonic Motion: [https://www.schoolphysics.co.uk/age16-19/Mechanics/Simple%20harmonic%20motion/text/Simple_harmonic_motion/index.html](https://www.schoolphysics.co.uk/age16-19/Mechanics/Simple%20harmonic%20motion/text/Simple_harmonic_motion/index.html) Accessed 13th April 2022
4. Simple Harmonic Motion: [https://courses.lumenlearning.com/physics/chapter/16-3-simple-harmonic-motion-a-special-periodic-motion/](https://courses.lumenlearning.com/physics/chapter/16-3-simple-harmonic-motion-a-special-periodic-motion/) Accessed 13th April 2022.
5. Simple Harmonic Motion: [https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/11.1/primary/lesson/simple-harmonic-motion-phys/](https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/11.1/primary/lesson/simple-harmonic-motion-phys/) Accessed 13th April 2022.

A simple harmonic motion (SHM) is a special type of oscillatory motion. In this chapter, we look into what SHM is and how it differs from other types of motion. 

 Simple Harmonic Motion Study Guide

# INTRODUCTION: 

You might have seen clocks like these used for antique or decorative purposes. We call it the pendulum clock. It has a dial that tells us the time, but a bob keeps swinging beneath it. Ever wondered why it moves like that? 🤔 Let's study the pendulum and its motion in more detail. 

![Pendulum clock ](//images.ctfassets.net/4yflszkpcwkt/6HY2vUpp9Gohge71XXeb6i/a2362270ce169a9ba912fd1949452f22/255px-Reloj_de_pendulo_Ansonia_C-1904.jpg) 
[Source](https://en.wikipedia.org/wiki/Pendulum_clock) 

## WHAT IS A PENDULUM?

A pendulum is a mass suspended from a pivot point that swings freely. When a pendulum is moved sideways from its resting equilibrium point, gravity acts as a restoring force, accelerating the pendulum towards its equilibrium position.  

![Simple gravity pendulum](//images.ctfassets.net/4yflszkpcwkt/45gFDqlhdHuxfIdFsFSlsv/263b68ea6b0a321662338487fa99b751/Simple_gravity_pendulum.svg.png) 
[Source](https://en.wikipedia.org/wiki/Pendulum)

- The restoring force acting on the pendulum's weight enables it to oscillate around the equilibrium position, swaying back and forth when released.  
- The period is the time it takes to execute one complete cycle, including both left and right swings.  
- The period is determined by the pendulum's length and, to a lesser extent, by the amplitude or swing breadth. 
- The equation for a pendulum's period T is: 
![Pendulum-s period](//images.ctfassets.net/4yflszkpcwkt/3z6VQNsAQpup5ylzUj6GSC/ed0261addc3105839efabf3981043927/Pendulum-s_period.png)
- The motion made by a pendulum is an example of periodic motion. Curious what is periodic motion? Let’s know more. 

## PERIODIC MOTION: 

- Periodic motion is defined as a motion that replicates itself at regular time intervals. 
- The motion by a pendulum can alternatively be classified as oscillatory. 
- An oscillatory motion occurs when the body travels back and forth around a fixed point. As a result, an oscillatory motion can be periodic but is not required. A special case of oscillatory motion is simple harmonic motion.

![Periodic Motion](//images.ctfassets.net/4yflszkpcwkt/5pJTYb9zMVjddIYcB8mgAe/9a32e76e94196ec984ae2722f2250ba4/13032.gif) 
[Source](https://www.toppr.com/ask/content/concept/periodic-and-oscillatory-motions-209174/)

## SIMPLE HARMONIC MOTION (SHM): 

- SHM is a type of oscillation with a straight line connecting the two extreme locations. 
- The entity's path must be a straight line. A restoring force would be oriented towards the equilibrium (or mean) position. 
- In simple harmonic motion, the mean position is a stable equilibrium. 
- (examples of SHM motion as models).

# CONCLUSION 

- Periodic motion is defined as a motion that replicates itself at regular time intervals. 
- Simple harmonic motion is a subset of periodic motion where the restoring force on a traveling entity works in the object's equilibrium point direction and is directly proportional to the object's displacement. 
- A pendulum is a mass suspended from a pivot point and may freely swing. 

## FAQs:

__1. How do pendulums work?__

A pendulum is a weight that is suspended from a reference point and goes back and forth due to gravity. With no external assistance, the swing remains to swing back and forth until resistance slows it down and finally stops it. 

__2. What does it mean when a pendulum swings?__

The restoring reaction force on the pendulum's mass enables it to swing about the mean position, swinging back and forth when released. The period is the time it takes to complete one complete cycle, including both left and right swings. 

__3. What is the simple pendulum theory?__

A basic pendulum comprises a mass m suspended on a string length L and a pivot point P. The pendulum is shifted to an initial angle and freed; it will swing back and forth regularly. 

*We hope you enjoyed studying this lesson and learned something cool about __Pendulum__! Join our Discord community to get any questions you may have answered and to engage with other students just like you! We promise, it makes studying much more fun!* 😎  

## SOURCES: 
1. 10.3 Pendulum. https://www.ck12.org/book/peoples-physics-concepts/section/10.3/. Accessed 10 Feb 2022. 
2. Pendulum. https://courses.lumenlearning.com/physics/chapter/16-4-the-simple-pendulum/. Accessed 10 Feb 2022. 


A pendulum is a weight that is suspended from a reference point and goes back and forth due to gravity. 


Pendulum Study Guide

### INTRODUCTION

This is an experience we are sure you’ve had- your favorite EDM track is blaring out of the speakers in your room, the bass drops, and all the furniture and windows rattle because of the sound. Your friend is on a swing in the playground, and you’re pushing harder with every cycle to send them higher. You then reach a point where it becomes effortless, and you only need to give a gentle nudge to keep the swing going to its full height. What if we told you the two examples are connected to the same concept in physics? Intrigued yet? Let’s learn about resonance! 

![Periodic Force](//images.ctfassets.net/4yflszkpcwkt/fpojuRlDm614kF9GIvjDH/de3d80c16e696c023d3f8b27e93dfe78/Periodic_Force.png)
[Source](https://www.northernhighlands.org/cms/lib/NJ01000179/Centricity/Domain/148/AA_CPO%20Text%20by%20chapter/Chapter%2019%20Harmonic%20Motion.pdf)

### VIBRATION AND HARMONIC MOTION 
Many objects around us vibrate or oscillate in a to-and-fro motion about a mean position. Examples include a pendulum, vibration of a guitar’s string, a weight suspended at the end of spring, etc. Whenever an object repeats its motion back and forth on the same path, it is in simple harmonic motion (SHM).  

![VIBRATION AND HARMONIC MOTION ](//images.ctfassets.net/4yflszkpcwkt/2nrDflPkTlD7sJ1T5HTV75/21f8060fc531a5d2b1a0cd7bdf48a8c2/figure1-1.png)
[Source](https://innovationandbeyond.wordpress.com/)

Consider the pendulum in the picture above.

- Every time the bob moves from one maximum position to the other, it completes one cycle.  
- The maximum displacement from the equilibrium position is called the amplitude of the pendulum. 
- The time the bob takes to complete one cycle is called the time period (T).  
- The number of cycles completed by the bob in 1 second is called the frequency (f) of the pendulum. 
- The concept of cycle, amplitude, time period and frequency applies to all types of vibrations from a swing in the playground to the strumming of a guitar and the music you play in your speakers.  

The mathematical relationship between frequency and time period is given by: 

![frequency and time period](//images.ctfassets.net/4yflszkpcwkt/5Z6eTyxbkRKkqbQwdhXilm/8ed3cf81b417cf021adc1372fcb6ca51/frequency_and_time_period.png)

Every pendulum (including the playground swing) has a frequency at which it swings when you give it a push. This is called the natural frequency of the pendulum. Mathematically it is calculated using the formula:

![Natural Frequency](//images.ctfassets.net/4yflszkpcwkt/5z1vcJK2s57ZkkTrUFRxE8/be77a750bfad1f3a2f4ee64c7ea8a71d/Natural_Frequency.png)

f = natural frequency in hertz 

g = acceleration due to gravity at 9.8 m/s2

L = length of pendulum in meters 

When you leave the swing undisturbed after one push, it continues to oscillate at its natural frequency. However if you continue pushing at the maximum during every cycle, the amplitude (height) of the swing continues to increase. This is when you send the swing (or pendulum) into a forced vibration by giving a periodic push to keep the oscillations going. 

### WHAT IS RESONANCE IN VIBRATION?

Suppose you pushed early before the swing reaches the maximum, you will slow it down (decrease the amplitude). Timing your periodic push to match the natural frequency is what is called resonance in physics. Resonance causes the amplitude of vibration to greatly increase.

More technically, every push you give is a periodic force. When the periodic force matches the natural frequency, the system is in resonance. All objects around us have a natural vibration frequency, including the furniture and windows in your house. When the music you play generates sound frequencies (which act as a periodic force) that are at the resonance frequency of the furniture, their amplitude suddenly increases, and you see them vibrating!

## CONCLUSION: 

- Whenever an object repeats its motion back and forth on the same path, it is in simple harmonic motion (SHM).   
- Simple Harmonic motion can be described by parameters such as cycles, periods, frequency, and amplitude. 
- The natural frequency is the frequency at which a system oscillates naturally. 
- Resonance occurs when the periodic force matches the natural frequency.

### FAQs:

__1. What is resonance? Give an example?__

Resonance occurs when the frequency of the periodic force matches the natural frequency of the system it is acting upon. Example: When loud music systems play in the lower frequencies, the windows and furniture in the room vibrate. This happens because some of the sound frequencies in the music track match the natural frequency of some of the objects in the house. 

*We hope you enjoyed studying this lesson and learned something cool about __Resonance__! Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our App to experience our fun, VR classrooms - we promise, it makes studying much more fun!* 😎 

### SOURCES: 

1. 11.3 Resonance with Sound Waves. https://www.ck12.org/book/ck-12-physics---intermediate/section/11.3/. Accessed 22 Feb 2022.  
2. The Physics of Resonance. http://www.intuitor.com/resonance/swings.html. Accessed 22 Feb 2022.  
3. Chapter 19 Harmonic Motion. https://www.northernhighlands.org/cms/lib/NJ01000179/Centricity/Domain/148/AA_CPO%20Text%20by%20chapter/Chapter%2019%20Harmonic%20Motion.pdf. Accessed 22 Feb 2022.  


The resonance vibration in a system causes the amplitude to magnify greatly. This article discusses the fundamentals of vibration, harmonic motion, and resonance.