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

2. 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

3. 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
Week after that (5/5)
Final: Monday May 5th, 1PM-3PM in this room
Physics 218, Lecture XXIV

4. 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

5. 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

6. Physics 218, Lecture XXIV

7. Physics 218, Lecture XXIV

8. 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

9. 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

10. 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

11. 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

12. 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

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

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

15. More Detail
Time
Physics 218, Lecture XXIV

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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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 and 18 will be on the final
I guarantee a problem from each
Physics 218, Lecture XXIV

29. End of Lecture Notes
Physics 218, Lecture XXIV

30. 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

31. 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 XXIV

32. 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

33. 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

34. 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