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) Lab Project Assignment introduced

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 Relation to Uniform Circular Motion Examples (Physlets)

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

7. Pendulums Simple pendulum –Equation of motion –Approximation sin(θ) ≈ θ Handout or Exercise –Solution Physical Pendulum Torsion Pendulum

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

9. 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

10. the end

11. 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

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

13. 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

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

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

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

17. Physlet E16.1 period vs. amplitude (spring and pendulum) Physlet E16.3 position and velocity Physlet E16.6 under, critical, overdamped Physlet E16.6 resonance (find f(resonant), m) 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

20. Physlet E16.3 position and velocity

21. A mass oscillates on a spring. Consider two possibilities: (i) v=0 and a=0 at some point in time. (ii) v=0 at some point, but a≠0 at that point. Which are true? 1)Both are. 2)Neither are. 3)Only (i) 4)Only (ii)

22. Which of the following functions satisfy the given differential equation? 1) 2) 3) 4) 5) 6)

23. Which of the following functions satisfy the given differential equation? 1) 2) 3) 4) 5) 6)

24. Which of the following functions satisfy the given differential equation? 1) 2) 3) 4) 5) 6)

25. Which of the following functions satisfy the given differential equation? 1) 2) 3) 4) 5) 6)

26. 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) A B C D E F

27. 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.

28. Rank on the basis of time to complete one cycle. (Least to greatest) A B C D E F

29. Rank according to maximum velocity. (Least to greatest) A B C D E F

30. Rank according to maximum acceleration. (Least to greatest) A B C D E F

31. Physlet E16.5,6 resonance

32. Physlet P16.3 Physlet P16.6

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

34. 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.

35. Which, if any, of the following functions satisfy the given differential equation? 1) 2) 3) 4) 5) 6)

36. Which, if any, of the following functions satisfy the given differential equation? 1) 2) 3) 4) 5) 6)

37. Which, if any, of the following functions satisfy the given differential equation? 1) 2) 3) 4) 5) 6)

38. Which, if any, of the following functions satisfy the given differential equation? 1) 2) 3) 4) 5) 6)

39. Physlet 16.12 Floating oscillator