1 / 20

Understanding Simple and Damped Harmonic Oscillators in Physics

This resource explores the concepts of simple and damped harmonic oscillators, focusing on the equations of motion, potential and kinetic energy, and mass-spring systems. It details the behavior of oscillators under different damping conditions including underdamped, critically damped, and overdamped regimes. Additionally, the implications of driven harmonic oscillators are discussed, emphasizing transient versus steady-state behavior under external forces. The content integrates mathematical modeling with practical examples, enhancing comprehension of complex oscillatory motions.

hedia
Télécharger la présentation

Understanding Simple and Damped Harmonic Oscillators in Physics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 321 Hour 11 Simple and Damped Harmonic Oscillators

  2. Find U and T Equilibrium Equation of motion ω, T Energy plot Mass on a Massless Spring y

  3. y Assume Find U and T Equation of motion ω, T x A Shallow Frictionless Bowl z

  4. y Assume Find U and T Newton’s Equations x Another Bowl z

  5. Lissajous.nb Example

  6. The equation: A little rearranging: Damped Oscillator A trial solution:

  7. Underdamped: • Critically damped: • Overdamped: Three Regimes

  8. Solution: or Underdamped

  9. Solution: Overdamped

  10. Solution: Critically Damped

  11. DampOsc5_4.nb Example

  12. Physics 321 Hour 12 Driven Harmonic Oscillators

  13. The equation: Let The oscillator wants to oscillate at but the driver forces it to oscillate at . This leads to transient vs steady state behavior! Driven Oscillator

  14. Driven_Osc.nb Example

  15. We assume a solution something like But So we employ a trick… The driving force is the real part of Driven Oscillator

  16. We assume a solution of the form This gives: Driven Oscillator

  17. Conclusion 1: Driven Oscillator

  18. Real parts: Imaginary parts: Driven Oscillator

  19. Conclusion 2: And finally the steady state solution is: Driven Oscillator

More Related