2. Chapter 14 Oscillations www.youtube.com/watch?v=Rlk59xdM_YY

3. Introduction Oscillations of a Spring (Hands-on emphasis) Simple Harmonic Motion (Mathematical emphasis) Pendulums - Simple & beyond simple Damped Harmonic Motion (Modeling emphasis) Driven Damped Harmonic Motion & Resonance (the grand finale)

4. Oscillations of a Spring Characteristics –Amplitude –Period –Frequency –Phase Discovery Lab (Handout) Question

5. Simple Harmonic Motion Mathematical Representation –Equation of motion (Simple common phenomenon using Classical Mechanics) –Solution exerciseexercise –Role of initial conditions –Phase angle –Angular frequency and frequency –Natural frequency –QuestionQuestion

6. …SHM cont’d. Relation to Uniform Circular Motion –Physlet I16.1 Usefulness –good approximation –component of any oscillation Physlet I16.5

7. Energy and SHM Kinetic energy of object in SHM Spring potential energy Physlet I16.3 Potential energy graphical representation –Whiteboard exercise Jeopardy problems 1 2 3 4 512345 Question

8. Pendulums Simple pendulum –Equation of motion –Approximation sin(θ) ≈ θ Handout Physlet I16.2 –Solution –QuestionQuestion Physical Pendulum –QuestionQuestion Torsion Pendulum

9. Damped Harmonic Motion Equation of motion and solution –Damping –Over-damped, Under-damped, Critical damping Physlet E16.6 Mathematical modeling –Stella model (later)

10. Driven Damped Harmonic Motion & Resonance Driven (Forced) situations Equation of motion and solution Mathematical modeling continued Resonance –What? and When? –Examples (including “field trip”) –Q-value Physlet E16.7

11. the end

12. Is the function Asin(ωt + ø) a solution of the general simple harmonic motion equation? If so, what are the constraints on ω, A and ø? back

13. To what question is this the answer? (1/2)(1kg)v 2 = (1/2)(2N/m)(.2m) 2 next back

14. To what question is this the answer? (1/2)(1kg)v 2 + (1/2)(1N/m)(-.2m) 2 = (1/2)(1N/m)(.4m) 2 next back

15. To what question is this the answer? (1/2)(3N/m)x 2 = (1/2)(1kg)(1m/s) 2 next back

16. To what question is this the answer? (1/2)(2N/m)(.2m) 2 = (1/2)(1N/m)x 2 next back

17. To what question is this the answer? (1/2)(1kg)(2m/s) 2 = (1/2)k(2m) 2 back

18. http://phet.colorado.edu/new/simulations/sims.php?sim=Masses_and_Springs

19. At the point P, the mass has _______ and _______. 1)v>0, a>0 2) v=0, a>0 3) v 0 4) v>0, a=0 5) v=0, a=0 6) v<0, a=0 7) v>0, a<0 8) v=0, a<0 9) v<0, a<0 back

20. 5N/m 1kg 0.4m stretch 1N/m 1kg 0.5m stretch 5N/m 2kg 0.2m stretch 4N/m 5kg 0.2m stretch 4N/m 4kg 0.5m stretch 1N/m 5kg 0.5m stretch Rank on the basis of time to complete one cycle. (Least to greatest) backback A B C D E F

21. A mass is hanging in equilibrium via a spring. When it is pulled down, what happens to the total potential energy (gravity + spring)? 1)It increases. 2)It stays the same. 3)It decreases. back

22. Physlet E16.5,6 resonance

23. Which falls faster? A: Meter stick B: Meter stick with heavy clamp 1)A 2)B 3)Same. 4)More info is needed. back

24. A pendulum is in an elevator that approaching the top floor of a building and is coming to a stop. What happens to the period of the pendulum? 1)It increases. 2)It stays the same. 3)It decreases. 4)More info is needed. back

25. angle in degrees angle in radians sine of angle tangent of angle cosine of angle 0.00.000 1.000 1.15.020 1.000 2.29.040.999 3.44.060.998 4.58.080.997 5.73.100.995 6.88.120.121.993 8.02.140.141.990 9.17.160.159.161.987 10.31.180.179.182.984 11.46.200.199.203.980 12.61.220.218.224.976 Trigonometric Functions for Small Angles back back