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

Checklist for Today Things due yesterday Chapter 15 & 16 in WebCT 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 WebCT Physics 218, Lecture XXIV

The Schedule This Week (4/21) Monday: Chapter 15 & 16 due in WebCT 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 WebCT Example final problems at http://faculty.physics.tamu.edu/toback/218/Lectures/FinalReview.pdf Week after that (5/5) Final: Monday May 5th, 1PM-3PM in this room Physics 218, Lecture XXIV

Next Semester Intro to Cosmology (PHYS289) 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 (PHYS289) 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

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 } Concepts } The math Physics 218, Lecture XXIV

Physics 218, Lecture XXIV

Physics 218, Lecture XXIV

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… Physics 218, Lecture XXIV

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

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

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

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

Questions What are the forces? Hooke’s Law: F= -kx Does this equation describe our motion? x = x0 + v0t + ½at2 Physics 218, Lecture XXIV

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

More Detail Time Physics 218, Lecture XXIV

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

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

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

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

Summary: Equation of Motion Mass m on a spring with spring constant k: x = A sin(wt + f) Where w2 = k/m A is the Amplitude is the “phase” (phase just allows us to set t=0 when we want) Physics 218, Lecture XXIV

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

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

Paper which tells us what happens as a function of time 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

Example: Spring with a Push We have a spring system Spring constant: K Mass: M Initial position: X0 Initial Velocity: V0 Find the position at all times Physics 218, Lecture XXIV

Simple Harmonic Motion What is MOST IMPORTANT? Simple Harmonic Motion X= A sin(wt + f) 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 XXIV

Exams Average all 3 Exams: 71% Mean of Exam 3 scores: 70.1% Took MPE3: 77.5% Didn’t take MPE3: 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 & WebCT quizzes 5 more points for getting 100 on the Mini-practice Exam final Physics 218, Lecture XXIV

Challenge Exam Not required (just for fun) Announcement of this semester’s 218 Challenge Exam: Monday April 28th 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 XXIV

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 5th, 1PM-3PM in this room Chapters 14 -16 and 18 will be on the final I guarantee a problem from each Physics 218, Lecture XXIV

End of Lecture Notes Physics 218, Lecture XXIV

Thursday Covers Chapter 8 through 11 Format similar to first two exams 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

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 25th: Exam 3 Thursday 27th: No lecture Thanksgiving No recitation Physics 218, Lecture XXIV

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

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 2nd law Begin review for the final, we’ll skip Chapter 15 Tuesday Dec 9th: Regular lecture More review for the final Monday Dec 15th: 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 XXIV

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