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Understanding Oscillatory Motion and Hooke's Law in Simple Harmonic Systems

This chapter delves into the key concepts of oscillatory motion, focusing on Hooke's Law and potential energy in springs. It covers simple harmonic oscillation and provides essential equations applicable to various systems like pendulums and tuning forks. The chapter discusses natural frequency, period, conservation of energy, and various damping scenarios—underdamped, overdamped, and critically damped systems. Additionally, it explores resonance in driven systems, highlighting practical applications and implications in real-world oscillatory phenomena.

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Understanding Oscillatory Motion and Hooke's Law in Simple Harmonic Systems

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Presentation Transcript

  1. Chapter 12 Oscillatory 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. Simple Pendulum

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

  17. Energy of SHO

  18. Conservation of Energy

  19. Energy of a pendulum (reminder)

  20. Energy of a pendulum

  21. Damped Oscillation

  22. Damping Force Fr

  23. Newton Second Law

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

  25. Under-damped

  26. Under-damped Movie

  27. Under-damped Over-damped Critically damped

  28. Under-damped Critically damped Over-damped

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

  30. Resonance Pushing a swing

  31. Driven / Forced Oscillations

  32. Resonance

  33. Resonance

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