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Basic Physics III Lecture 3

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so but today I want to start with little demonstration program that professor count the plan has kindly provided to
illustrate their damped harmonic motion post toward a simple harmonic this is a computer program that the inmates physics and right now so you can see that dialed in a mask of 10 kilograms spring constant 10 we don't know damn thing of all and so you see sort of the mosque on the on the spring and moving back and forth here and it's completely on band is surprise the position as a function of time so so right now the motion on them and their and therefore the empty told as functional time remains exactly the same so on this the position that can also turn on grounds off velocity and exhilaration and you actually can receive their media phase of the velocities it's a different rebel position velocity bases also did some amount of work so rich finally we can also look at we had a phase of the position itself as well as some the distances indicated indicating the amplitude of emotions and the angle with respect to the x axis the please and on is a functional time so I'll let us stop this real quick and not add a little bit of that Somalia can see that the amplitude as a function of time is reducing and as it will turn out to be an ample notice a function of time behaves like a like a exponential and eventually we particle comes basically stopped and cause velocity and acceleration decrees if the matter if we we increase the dampening further than that this will happen much more quickly after the we will only take us 1 or 2 cycles Fuller killer basically come less if you go still further 1st of all can notice that this period and seconds actually lost changes and increasing the damn thing to wear stronger then he becomes longer and longer for example now that would be almost not again as actually still a little bit of period union but you can basically already in a Nazi it anymore and if go total friction coefficient of 20 kilograms 2nd then there's not going to be a mail salacious left the position Graf just directly ghost 0 but don't swinging on size and his condition is called critical down and it is important for example former car shoppers always because that's what you want when you hit a bomb it doesn't take long to come to condition down the system further which do then after it still doesn't oscillate but it will take longer to reach it will take longer reached equilibrium position before this this exponential curve is having a lesson opened takes longer so we have basically 3 different behaviors 1 what's this was so Torre the Abbott goes a functional time 1 where there's no oscillation at all and the members of the limiting case so you're not all this described mathematically list what you just saw so terribly equation of motion as the book for the acceleration is the balloting term plus oscillatory divided by mask and that is nasty equation can actually transformed and relatively simple fact fiction farmers subject are general exponential behavior from about 8 part of each other a team and then each of those limited because these behavior of exponential can't just becomes a Powell each of his career this time seen on for should 1st KOM an 8 4 0 and so I want can transform it into a bit of form like that and now we we can see the different cases it this but he it's a negative than the quadratic equations solutions and in or what their case and that means that we can find some quantity that defines the scroll of the negative this 1 and then we can have a multiplication of exponential 1 using the damn thing feel with 2 M and 1 hour this on prime the critical back cases where this is and In which case a Z equals just down from and we get this however is this if this policy bigger than Zero situation doesn't have any solution and from what I told you um 2 days ago relations between exponential and functions and so what happens that Pace at trigonometric function of instead of the exponential function so I'll be gets the list damping terms the miners comity instead of a 2nd exponential like he'll get the proper articles function plus some angle and this armor triumph has the opposite whereas the opposite side that it's the so I dizzy Graf this now than that
the different cases just like in the program before we all want them case which takes a long time Yeager could here a clip critically damped 1 literature reaches equilibrium the fastest and Marianne every other case which also along approval but with told that this getting smaller and smaller and if draw lines around the yeah exponential function the miners gone too so
I have a bad thing is important in some systems you want to make it very small for example In the crop for all watch you wanted to use smallest possible so that it doesn't walk frequency and also that it doesn't cost as much energy to drop goal at other times however are bad is it is critical if you don't have any damn becomes really danger this is the case in the car shot the bad thing is provided by some business through it the week and those that viscous fluid once seen apart like that on the freeway and it was basically bouncing from little bump to build bomb on the freeway it makes it hot actually control come you don't want that and but is ideally want this the damping coefficient is won't but the chief critical damping Biffle and hit by a car comes steady state fast and therefore it becomes escape then of course another case would like things to be down In California some those crates of building has no damn thing at all the images how easy it to fall far more likely to get destroyed and the click of a damping building and in general they are down the building buildings you have to prevent so I let me now
I calculate an example with them and just using a tender for example is as follows a hell of a simple pendulum the length of 1 meter of dental simple it is that's really singing with small amplitude oscillations and after 5 minutes we are told is only half of what it was initially so the the question is what is the value of gamma for mulch and also what is the value of the Of the damping coefficient shift proportional and sewer and then the beet harvest by what factors 1st the bounce frequency from behind them and the answer is the equation of motion for the pendulum is basically just have to substitute variables so as if we have a Dell will not be the last of the spring constant Cheney and that helps us to find what is Dharma this Thomas over who just like was before being to and so we we see half the amplitude of the 3 300 seconds so that means that each the the miners dumb on-time 300 seconds must be 1 heart and if we take the laurel of this equation it became a soulful down and it turns out this is the moral tool divided by but 300 seconds and you get a value for all gone 0 . 0 0 2 2nd and that makes that would be coefficient Bell is what 1 1 8 0 0 1 0 0 0 0 460 meters so that is 1 half of the answer to this problem this example and the 2nd half this us frequency prime differ from on them and for that you use he can be relations between following up trial and Cahill and or in this case on prime so only crimes career this is a dual class the damping terms these cruel for most Soviet is value of cannot be all that we have before and here and we arrived at this value former Govs Times Square and former ghosts Graham the island and oscillation metal losses just this just she or the script so that's just 9 . 8 seconds career because Aswan and once we have always just with Omega Prime's can take the square will inform the racial and find out this ratio differs from 1 by 2 . 7 times 10 the modest so that is a very small and frequency ship and that is the reason for the smallest of the frequency shift that this is and is a very good possibly solar so damping tends to be small so the next thing we would like to consider what happens if I had a bad oscillations and applying a periodic and it gets increasingly more difficult Saunders case will spare you the math and just give me and the Soviets you want the patriotic driving force a frequency f or angular frequency on and but will you can define and natural frequency of an order residents frequency and do that as for sort both score on on so the air this is simply the spring constant Mosul a constant gravity the leg and if AFP is approximately equal to meaning that the the frequency of a driving force is roughly equal to that of a band that off cause also means a ongoing on both just multiply by to Pine then resonance or Croats and small forces current not also will try to demonstrative enough for is actually a resonant of you to solely with microphone I can make a fiddled songs With the help of this wasn't in this case naturally grown resonators and basically such residences or be a basis for most instruments most music residences current here Farmersville which I'm not when you actually can control the pitch because this resonator has multiple freak not what Seoul and other examples residents
astonishing before and freeway system can residents still the man I think of dangerous after leaving 1987 on 1 of the the big critics I wasn't saw are now after the fund will have do just that a just a little bit off or that we have the equation of motion wearing now added another term this obnoxious external costs which led to the bridge collapse for example and may find that he has resulted periodic motion frequency Of the driver or not Of the frequency of me down the sister not cockatiel and but the spirit of but the driving frequency and In case of residence is actually shifted by by 90 degrees for other cases the shifted by some time ago finds among can calculate the told of the oscillations like this expression and the attention of the final phase shift but this expression and 1 of a point or 2 if only qualitatively here that if you have a heavily damaged system that we have told is smaller than if you have a light system and the cars becomes infinite there's no doubt at all and also I read this residents of the called will will be narrower efforts if slightly down I really among can actually assignment quality factor of told the system which has caramel units it's given by the thing a natural frequencies and just the mask and among can completely characterized his residence and associated with the different quality by the way this curve seed which doesn't have a peek at all if only because that is the old whatever case when these just heavy down and Baker was slightly yeah members must the Soviet-backed will be the springs we you have this spring constant and a mosque so I can live now some O'Ryan is leader the chapter so they don't follow a simple harmonic motion which is characterized the forces proportional with displacement from acrylic room said there's a motion assignments until it has a period he pitches from profit from Congress crest there so that time to on the goal line cycle of oscillations then there are the the frequencies the inverse of the Senate's harmonies cycles per 2nd the empty told is the maximum displacement the observer the angle fine a sort of offset from given crest origin your and these the our core Angulo frequencies so tight times the frequency and omega is given by the racial spring constant and the abbot children face they depend on the initial conditions what happens at time because what displacement of loss the bomb but the visit that and you mean the time period and it it looks like this because I have unfortunately chosen the exact cause function but if this 1 was actually shifted a little bit at the end of the would be at the cracks so in general it for another picture but this is not just had this picture and or not so in this
case the period was still given by Brazil for example that but defiant in this final only goes to the origin but not so are a 2nd part B total energy of a simple harmonic motion a constant and it is comprised of became a comedic term and the potential images for the energy is constant told constant body changes back-and-forth between the kinetic and potential and In the case of the a simple pendulum American just replace Katie with a expiration of gravity and ends with the length the and and get the exact same form and therefore since got only depends on gravity and the length which is easy easy measurable commercial the acceleration of gravity if there's any kind of friction then that leads to let damped harmonic motion and In this case there are 3 categories Australasia across the system under them and then you have time dependent on which decreases exponentially a then that is not the most salacious opera or for critical dam removal would dampen in both cases the exponential decay heat displacement but they time to each equilibrium and lastly from external forces of lies and that the amplitude can get very large the frequency of the force is very close to the natural resonant may and that is called a resonance and among the dampening leads broader resonance that allow Japan to a broad of smaller 1 I'm going to conclude with a little traveled to of he says the next chapter purchase of old ways raise
related oscillations that something to do with oscillations but the ever mother Alma or you might wanna
move remove dark book so if I have taught wireline this then wave propagation on that wireless possible wait until it is quite indomitable and you can see a pulse traveling back and forth I'm getting reflected at the end and at as it turns out if you change the tension 1 of the men and rules and it takes longer for the year pulse to move back and forth the while this tight Of course if I tightened the wired much going to lose the corpse among commutable sold us and our problem our little
program tool makers easier to follow for people was sitting in the back so the interesting thing about the that reshaped sort of seems to be traveling this way but the actual role of course doesn't have otherwise a vote on court and Saudi a particle on the rope just oscillator up and down and in fact to see this for 1 particular value of X which is given by the current it changes vary between art and Don goes goes up and down and I can try and follow this a crest of the wave of smiles and you see that the displacement remained approximately constant but at a different position each time well it when I moved to any position on them on this graph and each part of the world only moves up and down so that all kinds of emotions 1 is the motion of the shape which seems to be traveling this and then perpendicular this is up-and-down motion and that is why they call this a transversely and exactly the same kind of place that excited you have thank you for your
intent
Erder
Greiffinger
Lunker
Bombe
Kraftfahrzeugexport
Reibantrieb
Schwingungsdämpfer
Bergmann
Konfektionsgröße
Besprechung/Interview
A6M Zero-Sen
Teilchen
Umlaufzeit
Oberschwingung
Schwingungsphase
Fahrgeschwindigkeit
Maske <Halbleitertechnologie>
Amplitude
Energielücke
Vakuumphysik
Multiplizität
Stunde
Relativistische Mechanik
Kaltumformen
Bleibergbau
Längenmessung
Tag
Urkilogramm
Übungsmunition
Elektronische Medien
Panzerung
Thermalisierung
Negativer Widerstand
Satzspiegel
Gummifeder
Ringgeflecht
Ersatzteil
Anstellwinkel
Walken <Textilveredelung>
Drosselklappe
Unterwasserfahrzeug
Bombe
Kraftfahrzeugexport
Armbanduhr
Uhr
Bergmann
Besprechung/Interview
Tonfrequenz
Armbanduhr
Übungsmunition
Leitungstheorie
Woche
Thermalisierung
Sprengring
Regentropfen
Astronaut
Speckle-Interferometrie
Schallabsorption
Bombe
Dschunke
Treiberschaltung
SEED
Cocktailparty-Effekt
Minute
Leitungstheorie
Feldhäcksler
Sonnenuhr
Gammabestrahlung
Amplitude
Eisenkern
Massenresonanz
Pulsationsveränderlicher
Crestfaktor
Massenresonanz
Messgerät
Übungsmunition
Säge
Werkzeug
Atmosphäre
Schiff
Tonhöhe
Anstellwinkel
Direkte Messung
Kraftfahrzeugexport
Güte <Schwingkreis>
Tonfrequenz
Amplitude
Auslenkung
Resonanzenergie
Chirp
Bildqualität
Nanometerbereich
Umlaufzeit
Pendel
Abend
Pendel
Energielücke
Kommandobrücke
Papierstaubung
Tonnenleger
Surfbrett
Relativistische Mechanik
Tonfrequenz
Basis <Elektrotechnik>
Metallschicht
Proof <Graphische Technik>
Rotverschiebung
Türglocke
Druckkraft
Band <Textilien>
Schiffsklassifikation
Negativer Widerstand
Grundfrequenz
Hall-Effekt
Umlaufzeit
Kondensatormikrophon
Gummifeder
Gammabestrahlung
Meson
Gel
Lithium-Ionen-Akkumulator
Schalter
Unterwasserfahrzeug
Nachwärmeabfuhr
Kaltumformen
Oberschwingung
Schwingungsdämpfer
Spannungsabhängigkeit
Tonfrequenz
Auslenkung
Kaliber <Walzwerk>
Resonanzenergie
Übungsmunition
Druckkraft
Feldeffekttransistor
Feldemissionsmikroskopie
Thermalisierung
Negativer Widerstand
Umlaufzeit
Innere Reibung
Ersatzteil
Amplitude
Speckle-Interferometrie
Negativer Widerstand
Mikrowellentechnik
Seil
Satzspiegel
Crestfaktor
Mikrowelle
Jahr
Ersatzteil
Lineal
Auslenkung
Werkzeugmacher
Teilchen

Metadaten

Formale Metadaten

Titel Basic Physics III Lecture 3
Serientitel Basic Physics III
Teil 3
Anzahl der Teile 27
Autor Smy, Michael
Lizenz CC-Namensnennung - Weitergabe unter gleichen Bedingungen 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen und nicht-kommerziellen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen und das Werk bzw. diesen Inhalt auch in veränderter Form nur unter den Bedingungen dieser Lizenz weitergeben.
DOI 10.5446/12965
Herausgeber University of California Irvine (UCI)
Erscheinungsjahr 2013
Sprache Englisch

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Fachgebiet Physik

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