Did you know, when bunjee jumping, a person undergoes simple harmonic motion? Learn more about this is this awesome unit which is loaded with 3D included, interactive study guides and simulations.

gravity force simulation screenshot

If physics has always been a point of interest to you but you’ve never known where to start, or how to structure your learning, our study guides are your best bet! Our physics study guides cover popular, important topics that can supplement your learning journey.  

Understand the concepts of photosynthesis, cellular respiration, enzyme reaction, with our interactive 3D models and study guides.

Do you rely on PMAT - the famous acronym to remember the stages of mitosis? That's a good strategy! We give you that and much more to ace your AP test through our study guides and interactive 3D models.

Understand Mendel's laws of heredity and how characteristics are passed down from parents to offspring. Discover more about his work in our informative study guides and associated 3D models.

Transcription, translation and replication, the 3 most important topics for any Biology student. Learn these and more with our interesting study guides and 3D models.

Always heard about the theory 'survival of the fittest'? Learn more of what it is based on with our informative study guides and interactive 3D models.

Explore the connection between plants, animals and the world around them through the study guides and interactive 3D models.

Get familiar with the structure and function of different cell organelles by using our interactive 3D models and study guides.

Learn about human physiology and complex organ systems with the help of our informative study guides and interactive 3D models.

More similar the DNA sequences of different organisms, the closer is the evolutionary relationship between them. Discover quirky facts about genetics and evolution with our interactive 3D models and study guides.

Explore the fascinating animal kingdom with our interactive study guides and 3D models. We do a deep dive into the evolution, classification, and behaviors with interactive 3D models.

Explore the structure, function, and behavior of cells in cell biology. Our interactive 3D models and detailed study guides will help you ace the exams!

Learn about the biosphere, ecosystems, habitats, populations, and communities with our interactive 3D model and study guides.

Evolution won't be a complex concept once you use Inspirit's engaging 3D models and detailed study guides.

Enter the fascinating world of genetics, the study of inheritance with our popular 3D models. Our easy-to-read study guides explain complex concepts in a super simple way!

Learn about human physiology and complex systems with the help of our interactive 3D models and informative study guides.

Deep dive into the human body and the organized and efficient human organ system. Let's learn about all this with the help of the following study guides and supporting 3D models.

Biology 101 for you! If biology has always been a point of interest to you, but you didn't know where to start, the comprehensive list of study guides and 3D models below are your best bet!

Learn and explore the characteristics of invertebrates with detailed study guides and very real 3D models.

Study the fascinating world of the plant kingdom learn about their structures, reproductive and growth processes. All of this delivered to you with our engaging 3D models.

Is a virus a prokaryote or eukaryote? Or neither? Or both? We'll help you answer that and much more via our fun and interactive study guides with loads of 3D models.

Like the cells of protists, the cells of fungi have cell walls. Wow! Explore more about the structure and function of protists and fungi in these study guides.

What are the distinguishing traits for different classes of vertebrates? No idea? Don't worry! We've got your back. Engage with our study guides and interactive 3D models to recognize these traits.

Learn about acids and bases, calculating pH, strong and a weak acids and bases, titration experiments, and more using our library of gamified study guides, 3D models, and interactive simulations.

Explore modern atomic theory by performing the experiments that established it, build your own atom in 3D, and use study guides and gamified challenges to become an expert on atomic structure!

Explore how biology and chemistry intersect all the way down at the molecular level using our extensive library of 3D, interactive content!

Compare the five major types of chemical reactions and learn how to write them in a balanced equation using our comprehensive study guides, gamified challenges, and interactive simulations!

Learn the rules of chemical nomenclature with the help of clear and comprehensive study guides, gamified challenges, and plenty of practice problems to make you a chemical classification pro!

Dive into this unit to learn about the types properties, and shapes of covalent bonds and the theories we use to explain why through comprehensive study guides, 3D models, and interactive simulations. 

Learn about electrical potential, voltaic cells, electrolysis, redox reactions, and more with the help of our easy-to-read study guides, interactive 3D models, and simulations.

Have you ever wondered why the atoms of different elements behave differently? Find out the science behind it with the help of our gamified study guides, 3D models, and interactive simulations.

Dive deeper into the concepts of entropy and free energy by exploring our comprehensive library of interactive 3D models, study guides, simulations, and more!

Learn about reversible reactions, chemical equilibrium, product constants, and more—all with the help of our immersive 3D study guides, models, and simulations.

Dive into one of the most exciting fields in science to learn about the the structure, composition, properties, and reactive characteristics of matter, all in 3D!

Explore the characteristics and properties of ionic and metallic bonds in an entirely new way using study guides, practice problems, and 3D, interactive simulations.

Check out our library of 3D study guides and simulations to understand important concepts in chemical kinetics like collision theory, activation energy, reaction order, catalysts, and more!

Everything is made of matter, but what is matter anyway? Learn about its composition, properties, and states in 3D and watch how they change with the help of our interactive models and simulations!

Learn about how different factors are measured, the units they use, and how they’re analyzed with our study guides, cheatsheets, worksheets, and more to master measurement in chemistry!

Dive into nuclear chemistry and engage with its concepts at the atomic level using our interactive 3D models and simulations!

Master orgo with the help of our extensive, 3D-rich library of resources to learn all about the structure, properties, composition, and reactive tendencies of organic compounds.

Learn to identify a redox reaction and balance its chemical equation using our extensive library of interactive content to learn everything you need to know (and more) about oxidation-reduction reactions!

Learn about the laws of solubility, molarity, molality, dilution, and more by exploring our 3D study guides, then apply what you learn by making your own solution in an interactive 3D simulation!

Learn about the states of matter using our detailed study guides and interactive 3D simulations that won’t only tell you how it works, but show you too.

Learn about the relationship between the reactants and products of a chemical reaction with the help of our study guides, practice problems, and simulations to make stoichiometry calculations a breeze.

Visualize periodic trends, atomic behavior, 3D orbitals, and more using an all-in-one, interactive periodic table customized just for you.

Master the mole and all of its applications in chemistry in no time with the help of our detailed study guides, 3D models, simulations, practice calculations, and more!

Become an expert on the ideal gas laws by exploring how pressure, volume, temperature, and particle count affect the behavior of a gas using our interactive simulations and 360° 3D models!

Dive into the details of changes in energy during phase changes and chemical reactions and visualize how thermochemical processes work with the help of our 3D models and interactive simulations.

Water might not seem that special, but it’s actually a rather unusual molecule in the world of chemistry. Check out our library of study guides, 3D models, and interactive simulations to find out why!

Why do the planets always revolve around the sun? Why hasn't there been a single instance where a planet has fallen? Find out with Inspirits interactive study guides, 3D models and simulations.

What do we think about when a vehicle collides with a wall? The damage caused? What about the transfer of energy? Use our interactive study guides and simulations and start thinking outside the box.

Use 3D models to understand energy, voltage, and the flow of electric current in a circuit. Play around with the simulations and refer to the study guides for this topics to make learning fun.

Prepare to get mind blown with our extensive set of resources to learn the concept of electric current. Take a look at our study guides, interactive 3D models, and simulations and pick your choice. 

A microwave oven and a telivision set require elctromagnetic radiation to function. Surprised? Walk into a world of such fascinating facts. Explore our 3D models, interactive study guides and simulations

Study about the unquie and fascinating concept of electromagnetism with our study guides and 3D models.

Have you heard of the scientist who ran naked on the road, shouting 'Eureka'? Want to know more about his discoveries that made him forget himself? Go visit our resourceful 3D library and learn more.

What are Laws of Motion? Who penned them down? Why are they important? Discover the answers to these and more questions with our user friendly study guides and associated 3D models.

Why are the planets always orbiting around the sun? Check out our physics study guides, 3D models and simulations, to get these and many more questions answered. 

Enter the fascinating world of magnets with our popular 3D models. Our easy-to-read study guides explain complex concepts in a super simple way!

Explore the world of modern physics through these study guides and interactive 3D models. 

Check out our rich interactive study guides and 3D models, to learn the physics of basketball, golf, javellin throw, and any other topic related to motion in 2D!

Ever wondered why trees appear to be moving backwards while you zoom past them on a highway? It's beacuse of motion in one-dimension. Explore more using our 3D rich study guides and interactive models.

These study guides extensively cover the differnt concepts of optical physics, they are supported with a bunch of almost real looking interactive 3D models, ray diagrams and simulations too. 

Why is the wheel always circular? Why wasnt it designed as a square or a traingle? Let's use Inspirit's extensive 3D rich library to learn more.

Do you own a pair of scissors, a jar with a lid and a bottle opener? Want to know how these are part of world of machines? Check out study guides, 3D models and simulations. 

Is sound and noise the same thing? Maybe yes, maybe no. Let's learn more with these study guides, interactive 3D models and more.

Explore the different cpncepts of static electricity with these interactive study guides, 3D models and simulations.

When a solid substance is heated, the particels vibrate and take up more space, causing expansion. Fascinating right??  Discover fun facts like this in our study guides and interactive 3D models.

AP Bio

CBSE Biology

CBSE Chemistry

CBSE Physics

CBSE Science

General Bio

General Chemistry

General Physics

## What Is Longitudinal Wave?

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

Sound propagates in the medium in the form of compressions and rarefactions. Longitudinal waves are waves in which the displacement of the medium is parallel to or opposite from the direction the wave travels, and the medium vibration is parallel to the direction the wave travels.

Each particle of matter vibrates about its normal rest position and along the axis of propagation in a longitudinal wave. All particles involved in the wave motion behave similarly, with the exception that there is a gradual change in the vibration's phase, which means that each particle completes its cycle of reaction at a different time. The result of the combined motions is the advancement of alternating compression and rarefaction areas in the propagation direction.

## Longitudinal Wave Formula

**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

### Sound Waves
A sound wave is created when energy moves through a medium, such as air, water, or any other liquid or solid material, creating a pattern of disruption that propagates away from the sound source. Sound waves are longitudinal waves.

### Pressure Waves

Pressure waves are produced when an object vibrates, such as a ringing phone, and these waves are the result of sound waves. The surrounding medium's particles are disturbed by the pressure wave, and those particles disturb the particles next to them, and so on.

## LONGITUDINAL WAVE DIAGRAM

![wave](//images.ctfassets.net/4yflszkpcwkt/3bs4ZF8tOc869x4VffZDMW/36198b8d4edbcce63db8641799ce7e05/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.

## Difference Between Longitudinal And Transverse 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!😎_

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

 Longitudinal Waves Study Guide

Acoustics

## What is Speed of a Wave? 
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)

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.

###Properties of Waves

 __1. Amplitude __

During wave motion particles oscillate about their mean position or equilibrium position to produce sound waves. The maximum displacement of the particles either above or below of the mean position is called amplitude or it can be said as Amplitude is the maximum height above or below from the mean position. Amplitude is denoted by X0 and the SI unit of amplitude is meter.

__2. Wavelength __

Transverse waves travel in consecutive or successive crest and trough while longitudinal waves travel in successive compression and rarefaction. In case of transverse waves the length of successive crust and trough is called its wavelength. While in case of longitudinal waves the length of successive compression and rarefaction is called its wavelength. Wavelength is denoted by the Greek letter lambda (λ) and its SI unit is meter.

__3. Time Period__

In order to understand the concept of time period we must understand the concept of wave cycle. In case of transverse waves one crust and one trough form one wave cycle or one oscillation while in case of longitudinal waves one compression and one rarefaction form one wave cycle or one oscillation. The total number of the wave cycles depend on the number of crust and trough in transverse waves whereas in the case of longitudinal waves it depends on the number of compressions and the rarefactions. The time taken by the oscillating body to complete one wave cycle or one oscillation is called time period. Time period is denoted by T and its SI unit is second. Example if a wave completes its oscillation or one wave cycle in two seconds than its time period is T = 2 seconds.

__4. Frequency__
The number of wave cycles or number of oscillations completed in one second. Frequency is denoted by f. The SI unit of frequency is hertz. Example if a wave completes three oscillations in one second then the frequency of that wave is three hertz. Frequency is the reciprocal of the time period. 

### Wave Speed Example

![speed](//images.ctfassets.net/4yflszkpcwkt/5ygQlyq43Lr9rw6xxynYQo/89fd2db79d3868195c4ee1cdfb9a9d13/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!😎_

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


Wave Speed Study Guide

# What is Simple Harmonic Motion?

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. 

![PENDULUM](//images.ctfassets.net/4yflszkpcwkt/ra6NQ49Bavm9XXO68H73G/2bd849dec237800bcb8b66aff0d18e43/pendulum_custom-40c376ae65462f2f44e1a84a115e90e768a235d1-s800-c85.webp)

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)

- 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. 

## 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)

- 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

### Difference Between Simple Harmonic, Periodic and Oscillation Motion

__Periodic Movement__

• After an equal amount of time has passed, a motion repeats itself. Consider a smooth circular motion.
• There is no place of balance.
• No restorative force exists.
• There is no steady state of balance.

__Oscillation Motion__

• A particle moving back and forth around a mean position is referred to as oscillatory motion when It travels on either side of the equilibrium or mean position.
• It is a particular kind of periodic motion that is limited by two extremes. Simple pendulum oscillation and the spring-mass system are two examples.
• The mean position (or equilibrium position) along any route is the location at which an item will continue to move while oscillating between two extreme positions around a fixed point. The route itself is not a restriction.
• A reliable equilibrium position is the mean position.

__SHM, or Simple Harmonic Motion__

• It is a particular instance of oscillation along a straight line between the two extreme locations (the path of SHM is a constraint).
• The route of the item must be a straight line.
• A restoring force will aim towards the equilibrium position (or average position).
• Simple harmonic motion has a stable equilibrium at the mean position.

### Simple Harmonic Motion Types
Simple Harmonic Motion, or SHM, may be divided into two categories:

• Linear SHM
• Angular SHM

__Simple Harmonic Linear Motion__

Simple harmonic motion is referred to when a particle oscillates in a straight line and around a set point (known as the equilibrium position).Consider a spring-mass system.

__Conditions for Linear SHM__
The restoring force or acceleration imposed on the particle should always be inversely proportional to the particle's displacement and pointed in the direction of the equilibrium position.

__ Angular Simple Harmonic Motion__

An angular simple harmonic motion occurs when a system oscillates angularly long with respect to a fixed axis.

__Conditions to Execute Angular SHM__

The restoring torque (or) angular acceleration exerted on the particle should always be proportionate to the particle's angular displacement and pointed in the direction of the equilibrium location.

__Simple Harmonic Motion Key Terms__

__Mean Position__

The location where there is no net force acting on the particle.

__SHM amplitude__

It is the particle's greatest deviation from the mean position.

__Time Period and SHM Frequency__

The time period is the least amount of time required to complete one oscillation, or it can alternatively be described as the minimum amount of time after which the particle continues to repeat its motion.
__T = 2π/ω__

Frequency is defined as the quantity of oscillations per second.

Angular frequency = 2πf = 2π/T and frequency = 1/T

__Phase in SHM__

The condition of a vibrating (or oscillating) particle with respect to its displacement and vibration direction at any given moment is known as the particle's phase.

### 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!😎_

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

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.


New to Inspirit? Check out our Getting Started Guide.

Explore Science in 3D and VR

Engage your students with models, simulations, and activities for your next class