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Chapter 14

Chapter 14. Periodic Motion. Hooke’s Law. Potential Energy in a Spring. See also section 7.3. Simple Harmonic Oscillator. Notations. This is the simple harmonic oscillation equation. Very very important!. You want to write ALL oscillation equations in this form. Simple pendulum.

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Chapter 14

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  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! You want to write ALL oscillation equations in this form.

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

  7. In general

  8. Rewriting Formulae Equations

  9. All equations looks the same 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

  19. 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. Damped Oscillation

  26. Damping Force Fr

  27. Newton Second Law

  28. Oscillations with damping

  29. Solving the Equation Try the solution:

  30. skip

  31. Skip

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

  33. Under-damped

  34. Under-damped Movie

  35. Three cases:

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

  37. Under-damped Over-damped Critically damped

  38. Under-damped Critically damped Over-damped

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

  40. Resonance Pushing a swing

  41. Driven / Forced Oscillations

  42. Amplitude A(ωd) Driven / Forced Oscillations

  43. Resonance

  44. Resonance

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