Physics 218 Lecture 24 Dr David Toback Physics

Physics 218 Lecture 24 Dr. David Toback Physics 218, Lecture XXIV 1

Checklist for Today • Things due yesterday – Chapter 15 & 16 in Web. CT • Things that are due Today – Chapter 18 reading • Things that are due Tomorrow – Chapter 18 problems as Recitation Prep • Tomorrow: – Recitation and Lab • Things due next Monday – Chapter 18 in Web. CT Physics 218, Lecture XXIV 2

The Schedule This Week (4/21) • Monday: Chapter 15 & 16 due in Web. CT • Tues: – Reading for Chapter 18 – Lecture on Chapter 18 • Wed: Recitation on Chapter 18, Lab • Thurs: Last lecture, Chapter 18 – Not covering Chapter 19 Next Week (4/28) • No lectures or recitations • Chapter 18 HW due in Web. CT • Example final problems at http: //faculty. physics. tamu. edu/toback/218/Lectures/Final. Review. pdf Week after that (5/5) • Final: Monday May 5 th, 1 PM-3 PM in this room Physics 218, Lecture XXIV 3

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” – Intro to Cosmology (PHYS 289) – 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 XXIV 4

Chapter 18: Periodic Motion • This time: – Oscillations and vibrations – Why do we care? – Equations of motion – Simplest example: Springs – Simple Harmonic Motion • Next time: – Energy } Physics 218, Lecture XXIV Concepts } The math 5

Physics 218, Lecture XXIV 6

Physics 218, Lecture XXIV 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” • Anything which is Periodic • Same as vibration • No new physics… Physics 218, Lecture XXIV 8

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 XXIV 9

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 Physics 218, Lecture XXIV 10

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 XXIV 11

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? k Physics 218, Lecture XXIV 12

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 XXIV 13

The forces No force Force in –x direction Force in +x direction Physics 218, Lecture XXIV 14

More Detail Time Physics 218, Lecture XXIV 15

Some Terms Amplitude: Max distance Period: Time it takes to get back to here Physics 218, Lecture XXIV 16

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 XXIV 17

Simple Harmonic Motion Call this type of motion Simple Harmonic Motion (Kinda looks like a sine wave) Next: The equations of motion: Use SF = 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 XXIV 18

Equation of Motion A block of mass m is attached to a spring of constant k on a flat, frictionless surface What is the equation of motion? k Physics 218, Lecture XXIV 19

Summary: Equation of Motion Mass m on a spring with spring constant k: x = A sin(wt + f) Where w 2 = k/m A is the Amplitude f is the “phase” (phase just allows us to set t=0 when we want) Physics 218, Lecture XXIV 20

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 XXIV 21

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 – What is the position of the mass at all times? – Where does the maximum speed occur? – What is the maximum speed? Physics 218, Lecture XXIV 22

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 XXIV 23

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 XXIV 24

What is MOST IMPORTANT? Simple Harmonic Motion X= A sin(wt + f) • What is points? • What is the the amplitude? phase? angular frequency? velocity at the end the velocity at the middle? Physics 218, Lecture XXIV 25

Exams • Mean of Exam 3 scores: 70. 1% – Took MPE 3: 77. 5% – Didn’t take MPE 3: 58. 5% – Average all 3 Exams: 71% Notes for the final: • No more “bonus” points • Problem 8 will consist of two items: – 5 points for getting 100% on all your homework & Web. CT quizzes – 5 more points for getting 100 on the Minipractice Exam final Physics 218, Lecture XXIV 26

Challenge Exam • Announcement of this semester’s 218 Challenge Exam: Monday April 28 th at 6: 00 PM – 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 Web. Site Physics 218, Lecture XXIV 27

Rest of This Week • Wednesday: Chapter 18 and Lab • Thursday: – Rest of Chapter 18 – Energy • Next Week: – No classes or Recitations – HW for Chapter 18 due • Final: Monday May 5 th, 1 PM-3 PM in this room – Chapters 14 -16 and 18 will be on the final – I guarantee a problem from each Physics 218, Lecture XXIV 28

Physics 218, Lecture XXIV 29

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 XXIV 30

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 email – No quiz • Tuesday 25 th: Exam 3 • Thursday 27 th: – No lecture Thanksgiving – No recitation Physics 218, Lecture XXIV 31

Next time • More on Oscillations: – Energy, Uniform Circular Motion, Pendulums • Last class is next Tuesday: – 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 XXIV 32

After next week • Tuesday Dec 2 nd: Rest of Chapter 14 – More on Oscillations – Energy, Uniform Circular Motion, Pendulums • Thursday Dec 4 th: Regular lecture – Kepler’s 2 nd law – Begin review for the final, we’ll skip Chapter 15 • Tuesday Dec 9 th: Regular lecture – More review for the final • Monday Dec 15 th: Final Exam, 1 PM. 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 XXIV 33

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 Physics 218, Lecture XXIV 34