Physics 218, Lecture XXII1 Physics 218 Lecture 22 Dr. David Toback

Physics 218, Lecture XXII2 Schedule for the Rest of the Semester Today: Chapter 13, Part 1 Thursday Nov. 30 th : Chapter 13, Part 2 Tuesday December 5 th : Final Exam Review No lecture on December 7 th (Reading day) Final exam is Monday, Dec. 11 th, 1-3PM We will skip Chapter 15

Physics 218, Lecture XXII3 Next Semester Many of you have asked about next semester: I am NOT teaching 208 However I am planning on teaching a new course: “Big Bang, Black Holes, No Math” –Introduction to Cosmology –Based on “A Brief History of Time” by Stephen Hawking –If you can’t take it, you might pass this info along

Physics 218, Lecture XXII4 Chapter 13: Periodic Motion This time: –Oscillations and vibrations –Why do we care? –Equations of motion –Our spherical cow: Springs –Simple Harmonic Motion Next time: –Energy –Uniform Circular Motion –Pendulums } Concepts } The math

Physics 218, Lecture XXII5

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7 What is an Oscillation? The good news is that this is just a fancy term for stuff you already know. It’s an extension of rotational motion Stuff that just goes back and forth over and over again “Stuff that goes around and around” Anything which is Periodic Same as vibration No new physics… just a combination of chapters 4/5 and 9/10

Physics 218, Lecture XXII8 Examples Lots of stuff Vibrates or Oscillates: –Radio Waves –Guitar Strings –Atoms –Clocks, etc… In some sense, the Moon oscillates around the Earth

Physics 218, Lecture XXII9 Why do we care? Lots of engineering problems are oscillation problems –Buildings vibrating in the wind –Motors vibrating when running –Solids vibrating when struck –Earthquakes → Moving towards setting up our spherical cow

Physics 218, Lecture XXII10 What’s Next 1.First we’ll “model” oscillations with a mass on a spring You’ll see why we do this later 2.Then we’ll talk about what happens as a function of time 3.Then we’ll calculate the equation of motion using the math

Physics 218, Lecture XXII11 k Simplest Example: Springs What happens if we attach a mass to a spring sitting on a table at it’s equilibrium point (I.e., x = 0) and let go? What happens if we attach a mass, then stretch the spring, and then let go?

Physics 218, Lecture XXII12 Questions What are the forces? Hooke’s Law: F= -kx Does this equation describe our motion? x = x 0 + v 0 t + ½at 2

Physics 218, Lecture XXII13 The forces No force Force in –x direction Force in +x direction

Physics 218, Lecture XXII14 More Detail Time

Physics 218, Lecture XXII15 Some Terms Amplitude: Max distance Period: Time it takes to get back to here

Physics 218, Lecture XXII16 Overview of the Motion It will move back and forth on the table as the spring stretches and contracts At the end points its velocity is zero At the center its speed is a maximum

Physics 218, Lecture XXII17 Simple Harmonic Motion Call this type of motion Simple Harmonic Motion (Kinda looks like a sine wave) Next: The equations of motion: Use  F = ma = -kx (Here comes the math. It’s important that you know how to reproduce what I’m going to do next)

Physics 218, Lecture XXII18 Equation of Motion A block of mass m is attached to a spring of constant k on a flat, frictionless surface Find the equation of motion k

Physics 218, Lecture XXII19 Summary: Equation of Motion Mass m on a spring with spring constant k: x = A sin(  t +  ) Where  2 = k/m A is the Amplitude  is the “phase” (phase just allows us to set t=0 when we want)

Physics 218, Lecture XXII20 Simple Harmonic Motion At some level sinusoidal motion is the definition of Simple Harmonic Motion A system that undergoes simple harmonic motion is called a simple harmonic oscillator

Physics 218, Lecture XXII21 Understanding Phase: Initial Conditions A block with mass m is attached to the end of a spring, with spring constant k. The spring is stretched a distance D and let go at t=0 Find the position of the mass at all times Where does the maximum speed occur? What is the maximum speed?

Physics 218, Lecture XXII22 Check: This looks like a cosine. Makes sense… Spring and Mass Paper which tells us what happens as a function of time

Physics 218, Lecture XXII23 Example: Spring with a Push We have a spring system –Spring constant: K –Mass: M –Initial position: X 0 –Initial Velocity: V 0 Find the position at all times

Physics 218, Lecture XXII24 What is MOST IMPORTANT? Simple Harmonic Motion x = A sin(  t +  ) What is the amplitude? What is the phase? What is the angular frequency? What is the velocity at the end points? What is the velocity at the middle?

Physics 218, Lecture XXII25 Challenge Exam Announcement of this semester’s 218 Challenge Exam: Monday December 4 th at 6:00PM –Not required (just for fun) –Does not (will not!!!) count as part of your final grade Test your skills against the best Aggies from all the Physics 218 sections (not just this lecture) on Physics 218 material Students who perform well will be recognized as Mechanics Scholars, and honored at a banquet in their honor. Other prizes, including cash. Handout information on my WebSite

Physics 218, Lecture XXII26 Exams Overall exam 3 Mean is an 69/100 3 Exam grades for semester (approx) have an average of 75%. Straight scale for A’s & B’s so far… (ballpark…)  >90% (247/275) A  >80% (220/275) B  >60% (152/275) C  >50% (138/275) D  <50% (138/275) F

Physics 218, Lecture XXII27 Next Week Wednesday: Chapter 12 HW and HWq due Recitation: Will cover Chapter 13 Thursday: –Rest of Chapter 13 –Energy, Uniform Circular Motion, Pendulums Next Tuesday: –Last day of class, Review for the final Monday December 11 th, 1-3PM: Final exam –HW for Chapter 13 due –Chapters 12 and 13 will be on the final and I guarantee a problem from each

Physics 218, Lecture XXII28

Physics 218, Lecture XXII29 Thursday Thursday: Exam 3 Covers Chapter 8 through 11 Format similar to first two exams Mini-practice exam is open and available for people who are caught up. Usual 5 points

Physics 218, Lecture XXII30 Coming up next week Monday: –Sections 513 and 514 will meet at their regular time/place –Section 515 and 516 have a exam review Monday evening. Time and room will be sent around via –No quiz Tuesday 25th: Exam 3 Thursday 27th: –No lecture Thanksgiving –No recitation

Physics 218, Lecture XXII31 Next time More on Oscillations: –Energy, Uniform Circular Motion, Pendulums Last class is next Tuesda y: –Review for the final Notes: –No recitation for Chapter 14 –HW for Chapter 14 is required –The material in Chapters 11 and 14 will all be on the final –I guarantee there will be at least one oscillations problem from these last two weeks on the final

Physics 218, Lecture XXII32 After next week Tuesday Dec 2nd: Rest of Chapter 14 –More on Oscillations –Energy, Uniform Circular Motion, Pendulums Thursday Dec 4th: Regular lecture –Kepler’s 2 nd law –Begin review for the final, we’ll skip Chapter 15 Tuesday Dec 9th: Regular lecture –More review for the final Monday Dec 15 th : Final Exam, 1PM. Here. –The material in Chapters 11 and 14 will all be on the final –I guarantee there will be at least one oscillations problem on the final

Physics 218, Lecture XXII33 About Today’s Lecture We’ll try something new: I’ll try to give an intuitive feel for the physics behind what we’re doing. I’ll try to give an intuitive feel for what happens in these types of problems We’ll do the math since the math gets it right There’s a fair amount of algebra/calculus so get ready! The good news is there’s very little which is new! Again we’re building on what we already know