Physics 218, Lecture XXIV1 Physics 218 Lecture 24 Dr. David Toback.

Physics 218, Lecture XXIV

1

Physics 218Lecture 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


The ScheduleThis 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 19Next 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


Next SemesterMany 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


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


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 motionStuff 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…


Examples

Lots of stuff Vibrates or Oscillates:–Radio Waves–Guitar Strings–Atoms–Clocks, etc…

In some sense, the Moon oscillates around the Earth


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


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


k

Simplest Example: SpringsWhat 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?


Questions

•What are the forces?Hooke’s Law: F= -kx

•Does this equation describe our motion?

x = x0 + v0t + ½at2


The forces

No force

Force in –xdirection

Force in +xdirection


More Detail

Time


Some Terms

Amplitude: Max distance

Period: Time it takes to get back to here


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


Simple Harmonic MotionCall 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)


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


Summary: Equation of Motion

Mass m on a spring with spring constant k:

x = A sin(t + )Where

2 = k/mA is the Amplitude is the “phase”

(phase just allows us to set t=0 when we want)



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


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?


Check:

This looks like a cosine. Makes sense… Spring and

MassPaper which

tells us what

happens as a

function of time


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


What is MOST IMPORTANT?


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?


Exams•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


Challenge Exam• 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


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


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


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


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


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


About Today’s LectureWe’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 XXIV1 Physics 218 Lecture 24 Dr. David Toback.

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Transcript of Physics 218, Lecture XXIV1 Physics 218 Lecture 24 Dr. David Toback.