Simple Harmonic Motion: Difference between revisions

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Claimed by Mary Francis McDaniel
Claimed by Mary Francis McDaniel


== Introduction ==
Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.


The two major components in Physics II are interactions between electric fields and magnetic fields. This broad subject focuses from a simple topic, electric fields to a much complex idea, electromagnetic radiation. Though this course is very broad in terms of materials that it covers, each topic is very important in understanding the phenomena of electric and magnetic interactions between particles (protons, electrons, dipoles, point charge, capacitor, and, etc), as omitting one concept out of hundreds of concept could lead one approaching the problem differently. This Wiki Page will discuss Chapter 21 of the Matters and Interactions Text Book, 4th edition (Patterns of Field in Space), specifically Gauss's Law and Electric Flux. In order to understand these concepts, one first need to understand the definition of electric field and know each component of Gauss's Law.
==The Main Idea==
== Dynamics ==


"Electric Flux" is a quantitative measure of the amount and direction of electric field over an entire surface of a specified object. There are two components in electric flux: direction of the electric field and magnitude of the electric field. These two sums up and give us the value, electric flux, which has a unit of Vm. In order to determine the direction of the electric field of an object, one need to figure out the x,y,z coordinates of the faces of an object and then calculate the normal vector that comes out of the surface. Secondly, to determine the direction of the electric field of an object, one first need to know the number of dimensions of an object (i.e: 6 faces in a rectangular prism) and areas for each face of the object. Finally, one should be able to calculate the electric flux of an object by multiplying the electric field at a location on each surface of the box by corresponding normal vector and multiplying this value by the area of the surface that was just calculated. One must repeat this process the remaining surfaces (faces) and by adding up all electric flux, that will be the electric flux of the object one wanted to calculate. This value is essential because it will be useful for calculating total charged enclosed inside the object later on. The above written method of calculating electric flux may be confusing at first, but knowing the Gauss's Law, being able to apply this Law to the real problem, and by going through the example below should make sure understanding of this concept.
Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats.  


== Energy ==
The Gauss's Law simplifies definition of "Electric Flux" into a one simple equation.


===A Mathematical Model===


[[File:Gauss.JPG]]
What are the mathematical equations that allow us to model this topic.  For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.


 
===A Computational Model===
[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html Gauss's Law]
 
[http://www.colorado.edu/physics/phys1120/phys1120_sp08/notes/notes/Knight27_gauss_lect.pdf Gauss's Law Examples]
 
====??====


How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
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===Simple===
===Simple===
[[File:BBB.PNG]]
Electric flux on the disk, by using Gauss's Law, is the multiplication between Electric Field normal to the disk's surface and surface area of the disk.
Electric Field Normal to the Surface: E x sin(40) = 327 V/m x sin(40)
Surface Area of the disk: 3.14 x 0.02 x 0.02 m^2
Electric Flux on the Disk: 327 V/m x sin(40) x 3.14 x 0.02 x 0.02 m^2 = 0.264 Vm
===Middling===
===Middling===
The electric field has been measured to be vertically upward everywhere on the surface of a box 20 cm long, 4 cm high, and 3 cm deep, shown in the figure. All over the bottom of the box E1 = 1100 V/m, all over the sides E2 = 950 V/m, and all over the top E3 = 750 V/m.
[[File:sss.JPG]]
Since E1, E2, and E3, are all measured to be vertically upward everywhere on the surface of a box, only the bottom surface and the top surface will be focused (multiplying the normal vector of other surfaces than the bottom and top surfaces will result in zero electric flux). The normal vector of the bottom surface is known to be <0,-1,0> and that of the top surface is known to be <0,1,0> assuming vertically upward is in +y direction.
E1 = <0, 1100, 0> V/m,
E2 = <0, 950, 0> V/m,
E3 = <0, 750, 0> V/m,
E1 corresponds to the bottom surface according to the diagram. Multiplying vector E1 with its normal vector of the bottom surface equals -1100 (dot product), and multiplying this vector by the area equals -1100 V/m x 0.20 m x 0.03 m = -6.6 Vm.
E3 corresponds to the top surface according to the diagram. Multiplying vector E3 with its normal vector of the top surface equals 750 (dot product) and multiplying this vector by the area equals 750 V/m x 0.20 m x 0.03 m = 4.5 Vm.
Therefore, the sum of the electric flux in this box equals -6.6 Vm + 4.5 Vm = -2.1 Vm
To determine the amount of charge enclosed by the box, we use Gauss's Law. Since we know the sum of the electric flux, in order to find q (inside the box) we just have to multiply summed electric flux and epsilon naught (8.85 e-12 unit)
Total Charge: -2.1 x 8.85 x 10 ^ (-12) = -1.8585 x 10 ^ (-11) C
===Difficult===
===Difficult===
[[File:AAA.JPG]]
To calculate the electric flux you will have to know the normal vector or the electric field in normal direction of each side of the cube.
There are only two sides affecting the net electric flux on this cubical surface, bottom face and right-handed side face (rest will be zero).
Normal Electric Field (Bottom Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm
Normal Electric Field (Right-Handed Side Face): E1 x sin(27) = 400 V/m x sin(27) x 0.35m x 0.35m = 22.2455 Vm
Net Electric Field = 44.49 Vm
Net Charge inside the cubical surface = 44.19 Vm x 8.85 x 10 ^ (-12) = 3.94 x 10 ^ (-10) C


==Connectedness==
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#How is it connected to your major?
I am majoring in Materials Science and Engineering and going further on from Electric Flux, there is a way to calculate Electric Flux Density (D). To obtain D, you have to multiply epsilon (permittivity) of the material to the Electric Field, E. Of course, different materials will have different Electric Flux. For example there are three major types of materials: insulator, semi-conductor, and conductor. Depending on their uses, you would want to make sure that the material of the desired product does not contain electric flux due to excess charge on the surface. This is the reason that electric flux and total charge of the closed surfaced objects are useful when as an engineer you want to think what type of properties you would desire for your product.
#Is there an interesting industrial application?
#Is there an interesting industrial application?


==History==
==History==


Thermodynamics was brought up as a science in the 18th and 19th centuries. However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer.  G. Black first introduced the word 'thermodynamics'.  Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat.  The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot.  He is often known as "the father of thermodynamics".  It all began with the development of the steam engine during the Industrial Revolution.  He devised an ideal cycle of operation.  During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics.  In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics.  Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium.
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.


== See also ==
== See also ==
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Books, Articles or other print media on this topic
Books, Articles or other print media on this topic
[http://www.phys.utk.edu/daunt/EM/PDF/SJDLecture22.pdf Electric Field and Gauss's Law]


===External links===
===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]


Internet resources on this topic


==References==
==References==


https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
This section contains the the references you used while writing this page
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/


[[Category:Interactions]]
[[Category:Which Category did you place this in?]]

Revision as of 18:02, 4 December 2015

Claimed by Mary Francis McDaniel

Simple harmonic motion is an approximation that ignores friction and air resistance. Although this assumption can often not be made in everyday calculations, simple harmonic motion can approximate these otherwise complicated situations, fairly well. Simple harmonic motion can be used to estimate many systems including spring-mass systems and the swinging of a pendulum in certain instances which will be explained in further detail below. This Wiki Page will discuss simple harmonic motion which is discussed in detail in Chapter Four: Contact Interaction.

The Main Idea

Simple harmonic motion is a periodic motion, a motion that is repeated over some time interval. This periodic motion has a restoring force, a force that is always working to return the system to equilibrium position, that is proportional and opposite to displacement. Due to this as the system gets farther from equilibrium position the larger the force is to return it to equilibrium position. When no friction or air resistance is present the system will continue to oscillate as the restoring force decreases as the object gets closer to equilibrium position until the force reaches zero, but at which point the particle continues due to its initial momentum until passes equilibrium position. Then the restoring forces increases in the opposite direction until the momentum is changed enough to change the direction of the particle and the process repeats.


A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Middling

Difficult

Connectedness

  1. How is this topic connected to something that you are interested in?
  2. How is it connected to your major?
  3. Is there an interesting industrial application?

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

[1]


References

This section contains the the references you used while writing this page

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