1. Physics 104 – Spring 2017 Intro and Harmonic Oscillator Energy
Introduction and Syllabus
Procedures (same as 103)
Topics covered
Differences with Phy 103
Harmonic Oscillator
Moscow, Russia December 2016

2. General Physics: Thermodynamics, Electromagnetism, Optics
Intro and Syllabus
Physics 104
General Physics: Thermodynamics, Electromagnetism, Optics
Spring 2016 Syllabus
Instructor: Nat Hager, Research Scientist, Physics and Engineering
173 Masters/Esbenshade (behind mineral gallery)
- 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 Home: before 9:00 PM. Please leave a message.
Class Hours: Tue/Thu/Fri 11:00 AM – 12:20 PM Esbenshade 270
All class periods are the same format. Discussion topics will be covered in all sessions.
Lab: Thu :00 – 3:50 PM or 4:00 – 5:40 PM
Office Hours: Tuesday, Friday 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.
Prerequisites: Physics 103 or equivalent
Textbook: Giancoli, D.C., Physics, Seventh Edition, Prentice Hall, 2014.
Supplemental Texts: Many Resources in the Physics Hideaway in Esbenshade
including: Boyle, J, Study Guide: Physics (Giancoli), Prentice Hall, 2004.

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

4. Topics Waves and Sound (Ch. 11-12) Thermodynamics (Ch. 13-15)
Electricity and Magnetism (Ch )
Optics (Ch. 23)
We’re trying to cover a lot,
so we’ll have to skip around some.
(almost never do starred sections)

5. 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 𝐹=𝑞𝐸
Magnetic 𝐹=𝑞𝑣×𝐵
But use same F = ma relations
Reinterpret old concepts
Gravitational Field g= 9.8 𝑁 𝑘𝑔 (𝑠𝑎𝑚𝑒 𝑎𝑠 𝑚 𝑠 2 ) F=mg
Electric Field 𝐸= 𝑥𝑥 𝑁 𝐶 F=𝑞𝐸
Magnetic Field 𝐵= 𝑥𝑥 𝑁 𝐴 ∙𝑚 F=qv×𝐵
Develop analogous methods
Flow of fluid (continuity) -> flow of electrical current (Kirchoff)

6. Simple Harmonic Oscillator
A little Physics 103
Jumping-off point for Waves

7. 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

8. Energy in Harmonic Oscillator
Potential Energy
Work done by relaxing spring:
(force x distance)
𝑊= 𝑥 𝑖 𝑥 𝑓 −𝑘𝑥 𝑑𝑥=− 1 2 𝑘 𝑥 𝑓 2 − 1 2 𝑘 𝑥 𝑖 2
Looks like decrease in potential energy
Kinetic Energy
Energy gained by block being pushed:
𝑊= 1 2 𝑚 𝑣 𝑓 2 − 1 2 𝑚 𝑣 𝑖 2
Appears as increase in kinetic energy
Total Energy
Loss of potential = gain in kinetic, vice-versa
Sum of Kinetic and Potential Constant
𝐸= 1 2 𝑚 𝑣 𝑘 𝑥 2 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Limiting points 𝐸= 1 2 𝑚 𝑣 𝑚𝑎𝑥 𝐸= 1 2 𝑘 𝐴 2

9. 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

10. Example 11-4 - Part 1 Vertical - Find spring constant 𝐹 𝑦 =0
𝐹 𝑦 =0
𝑘 𝑥 𝑜 −𝑚𝑔=0
𝑘= 𝑚𝑔 𝑥 𝑜 = 0.3 𝑘𝑔 9.8 𝑚 𝑠 𝑚
𝑘=19.6 𝑁 𝑚

11. Example 11-4 - Part 2 Horizontal - Find total energy
𝐸 𝑡𝑜𝑡 = 1 2 𝑘 𝑥 𝑚 𝑣 2
At maximum amplitude A
𝐸 𝑡𝑜𝑡 = 𝟏 𝟐 𝒌 𝒙 𝟐 𝑚 𝑣 2 = 1 2 𝑘 𝐴 2
𝐸 𝑡𝑜𝑡 = 𝑁 𝑚 𝑚 2
𝐸 𝑡𝑜𝑡 =0.098 J

12. Example 11-4 - Part 3 At x=0 - maximum velocity vmax
𝐸 𝑡𝑜𝑡 = 1 2 𝑘 𝑥 2 + 𝟏 𝟐 𝒎 𝒗 𝟐 = 1 2 𝑚 𝑣 𝑚𝑎𝑥 2
0.098 𝐽=𝐸 𝑡𝑜𝑡 = 1 2 𝑚 𝑣 𝑚𝑎𝑥 2
𝑣 𝑚𝑎𝑥 = 2 ∙0.098 𝐽 0.3 𝑘𝑔 =0.81 𝑚 𝑠
At x= velocity
𝐸 𝑡𝑜𝑡 =0.098 𝐽
𝑃𝐸= 𝑁 𝑚 𝑚 2 =.0245 𝐽
𝐾𝐸=0.098 𝐽− 𝐽= 𝐽
1 2 𝑚 𝑣 2 = 𝑣=0.7𝑚/𝑠

13. Example 11-4 - Part 4 Maximum acceleration at maximum stretch 𝑎= 𝑘𝐴 𝑚
𝐹=𝑚𝑎=𝑘𝑥=𝑘𝐴
𝑎= 𝑘𝐴 𝑚
𝑎= 𝑁 𝑚 0.1 𝑚 0.3 𝑘𝑔
𝑎=6.53 𝑚 𝑠 2

14. Example – Problem 23 𝐸 𝑡𝑜𝑡 = 1 2 𝑘 𝑥 2 + 𝟏 𝟐 𝒎 𝒗 𝟐 = 1 2 𝑚 𝑣 𝑚𝑎𝑥 2
At center point A
𝐸 𝑡𝑜𝑡 = 1 2 𝑘 𝑥 2 + 𝟏 𝟐 𝒎 𝒗 𝟐 = 1 2 𝑚 𝑣 𝑚𝑎𝑥 2
𝐸 𝑡𝑜𝑡 = 𝑘𝑔 𝑚 2
𝐸 𝑡𝑜𝑡 =3.31 J
Amplitude
3. 31 𝐽=𝐸 𝑡𝑜𝑡 = 1 2 𝑘 𝐴 2
𝐴= 2 ∙3.31 𝐽 124 𝑁 𝑚 =0.231 𝑚

15. Example – Problem 13 At any point x Amplitude Max velocity
𝐸 𝑡𝑜𝑡 = 𝟏 𝟐 𝒌 𝒙 𝟐 + 𝟏 𝟐 𝒎 𝒗 𝟐
𝐸 𝑡𝑜𝑡 = 𝑁 𝑚 𝑚 𝑘𝑔 𝑚 𝑠 2
𝐸 𝑡𝑜𝑡 =0.056 J J =0.51 J
Amplitude
0. 51 𝐽=𝐸 𝑡𝑜𝑡 = 1 2 𝑘 𝐴 𝐴=.06 𝑚
Max velocity
0. 51 𝐽=𝐸 𝑡𝑜𝑡 = 1 2 𝑚 𝑣 𝑚𝑎𝑥 𝑣 𝑚𝑎𝑥 =.58 𝑚 𝑠

16. Vertical Harmonic Oscillator

17. Summary - Harmonic Oscillator Energy
At any position
𝐸= 𝟏 𝟐 𝒎 𝒗 𝟐 + 𝟏 𝟐 𝒌 𝒙 𝟐
At full amplitude:
𝐸= 1 2 𝑚 𝑣 2 + 𝟏 𝟐 𝒌 𝒙 𝟐 = 1 2 𝑘 𝐴 2
At max-velocity midpoint:
𝐸= 𝟏 𝟐 𝒎 𝒗 𝟐 𝑘 𝑥 2 = 1 2 𝑚 𝑣 𝑚𝑎𝑥 2
Same for all 3: find for one case, know it for all.
Find total energy, find one component, subtract for other.

18. Harmonic Oscillator- Tip
Do not waste time memorizing this stuff:
𝑣=± 𝑣 𝑚𝑎𝑥 1− 𝑥 2 𝐴 2
You don’t need it
You’ll soon forget it.
It trivializes the underlying physics
Instead Learn
𝐸=𝐾𝐸+𝑃𝐸
and how KE and PE just get swapped back and forth!