1. Chapter 14 Periodic Motion

2. Hooke’s Law

3. Potential Energy in a Spring See also section 7.3

4. Simple Harmonic Oscillator

5. Notations This is the simple harmonic oscillation equation. Very very important! ALL You want to write ALL oscillation equations in this form.

6. Other Examples Simple pendulum Tuning fork Skyscraper (Inverted Pendulum)

7. In general

8. Rewriting Formulae Equations

9. All equations looks the same ALL You want to write ALL oscillation equations in this form.

10. Solution

11. (Natural) Frequency, Period, etc…

12. Example

13. What it looks like

14. x,v & a

15. Using initial conditions

16. Example Given moment of inertia I and CM at l, find the angular frequency.

17. Example

18. Simple Pendulum

20. Example A lead ball is attached to a string 3m long. Find the natural period of the pendulum.

21. Energy of SHO

22. Conservation of Energy

23. Energy of a pendulum (reminder)

24. Energy of a pendulum

25. DampedOscillation

26. Damping Force FrFr

28. Newton Second Law

29. Oscillations with damping

30. Solving the Equation Try the solution:

31. skip

32. Skip

33. Under-damped Over-damped Critically damped Three Cases

34. Under-damped

35. Under-damped Movie

36. Three cases: 1. 2. 3. 

37. Under-damped: Over-damped: Critically damped: Three Cases

38. Under-damped Over-damped Critically damped

39. Under-damped Critically damped Over-damped

40. under damped over damped critically damped system slows down fastest when critically damped Too much damping Is counter-productive!

41. Resonance Pushing a swing

42. Driven / Forced Oscillations

43. Amplitude A(ω d )

44. Resonance