Physics 104 – Spring 2014Intro and Harmonic Oscillator Energy

• Maglev Tour– Magnetic force

www.win.net/~dorsea/nehager/south/atlanta_maglev.htm

• Introduction and Syllabus

• Procedures (same as 103)

• Topics covered

• Differences with Phy 103

• Harmonic OscillatorAmerican Maglev Technology, Inc. Jan 2011Powder Springs, GA

Intro and Syllabus

Physics 104General Physics: Thermodynamics, Electromagnetism, Optics

Spring 2014 Syllabus• • Instructor: Nat Hager, Research Scientist, Physics and Engineering• 173 Masters/Esbenshade (behind mineral gallery)• • Email: nehager@msi-sensing.com - also forwards to smartphone. (OK to nag if I don’t reply in a day or 2). • • Web: msi-sensing.com/etown.htm or public directory “hagerne”• • Phone: Office/Lab 361.1377. Home: 898.3053 before 9:00 PM. Please leave a message.• • Office Hours: Monday, Tuesday 1:00 – 2:00 PM• Or by appointment. Please feel free to stop by my lab anytime, if my door is closed please leave a note.• • Class Hours: Mon/Tue/Fri 11:00 AM – 12:20 PM• All classes in Nicarry 228. All class periods are the same format. Discussion topics will be covered in all sessions.• • Lab: Tue/Fri 2:00 – 3:50 PM • • Prerequisites: Physics 103 or equivalent• • Textbook: Giancoli, D.C., Physics, Sixth Edition, Prentice Hall, 2004.• • Supplemental Texts: Many Resources in the Physics Hideaway in Esbenshade• including: Boyle, J, Study Guide: Physics (Giancoli), Prentice Hall, 2004.

Procedures

• Same as Physics 103– WebAssign (setup)– Quizzes (5)– Exams (3)– Lab– Final– Powerpoints– Equation sheets

Topics

• Waves and Sound (Ch. 11-12)• Thermodynamics (Ch. 13-15)• Electricity and Magnetism (Ch. 16-22) • Optics (Ch. 23)

We’re trying to cover a lot, so we’ll have to skip around some.

(almost never do starred sections)

General Differences with Physics 103• Use “Energy” in broader context

– Kinetic energy of ideal gas. (6.02 x 1023 molecules)– Potential energy stored in chemical bonds (fuel).– Energy stored/carried in EM field. – Anything that can do work!

• Define new Forces– Electrostatic – Magnetic – But use same F = ma relations

• Reinterpret old concepts– Gravitational Field – Electric Field – Magnetic Field

• Develop analogous methods– Flow of fluid (continuity) -> flow of electrical current (Kirchoff)

Simple Harmonic Oscillator• A little Physics 103

• Jumping-off point for Waves

Simple Harmonic Oscillator• Object subject to restoring force around equilibrium:

F = - kx– Force proportional to and opposite displacement– Oscillatory motion around equilibrium – Rate determined by mass m and k – Frictional damping

• Examples– Block on a spring (car on springs)– Meter stick anchored one end (diving board)– String in guitar (sound wave)– Object bobbing in water– Molecule in crystal lattice

Energy in Harmonic Oscillator• Potential Energy

– Work done by expanding spring:– (force x distance)

– Looks like decrease in potential energy

• Kinetic Energy– Energy gained by block being pushed:

– Appears as increase in kinetic energy

• Total Energy– Loss of potential = gain in kinetic, vice-versa– Sum of Kinetic and Potential Constant

– Limiting points

Harmonic Oscillator Terminology

• Cycle – One complete oscillation

• Amplitude – x = -A to x = +A

• Period – time to make one cycle

• Frequency – # cycles per second

• Frequency vs. Period– f = 1/T– T = 1/f

Example 11-4 - Part 1

• Vertical - Find spring constant

Example 11-4 - Part 2

• Horizontal - Find total energy

• At maximum amplitude A

Example 11-4 - Part 3• At x=0 - maximum velocity vmax

• At x= 0.05 - velocity

Example 11-4 - Part 4

• Maximum acceleration at maximum stretch

Example – Problem 23

• At center point A

• Amplitude

Example – Problem 13

• At any point x

• Amplitude

• Max velocity

Vertical Harmonic Oscillator

Summary - Harmonic Oscillator Energy• At any position

• At full amplitude:

• At max-velocity midpoint:

• Same for all 3: find for one case, know it for all.

• Find total energy, find one component, subtract for other.