1 / 30

Chapter 13 Oscillatory Motion

Chapter 13 Oscillatory Motion. Heinrich Hertz (1857-1894). Periodic motion Periodic ( harmonic ) motion – self-repeating motion Oscillation – periodic motion in certain direction Period (T) – a time duration of one oscillation

aviv
Download Presentation

Chapter 13 Oscillatory Motion

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. Chapter 13 Oscillatory Motion

  2. Heinrich Hertz (1857-1894) • Periodic motion • Periodic (harmonic) motion – self-repeating motion • Oscillation – periodic motion in certain direction • Period (T) – a time duration of one oscillation • Frequency (f) – the number of oscillations per unit time, SI unit of frequency 1/s = Hz (Hertz)

  3. Simple harmonic motion • Simple harmonic motion – motion that repeats itself and the displacement is a sinusoidal function of time

  4. Amplitude • Amplitude – the magnitude of the maximum displacement (in either direction)

  5. Phase

  6. Phase constant

  7. Angular frequency

  8. Period

  9. Velocity of simple harmonic motion

  10. Acceleration of simple harmonic motion

  11. Chapter 13 Problem 19 Write expressions for simple harmonic motion (a) with amplitude 10 cm, frequency 5.0 Hz, and maximum displacement at t = 0, and (b) with amplitude 2.5 cm, angular frequency 5.0 s-1, and maximum velocity at t = 0.

  12. The force law for simple harmonic motion • From the Newton’s Second Law: • For simple harmonic motion, the force is proportional to the displacement • Hooke’s law:

  13. Energy in simple harmonic motion • Potential energy of a spring: • Kinetic energy of a mass:

  14. Energy in simple harmonic motion

  15. Energy in simple harmonic motion

  16. Chapter 13 Problem 34 A 450-g mass on a spring is oscillating at 1.2 Hz, with total energy 0.51 J. What’s the oscillation amplitude?

  17. Pendulums • Simple pendulum: • Restoring torque: • From the Newton’s Second Law: • For small angles

  18. Pendulums • Simple pendulum: • On the other hand

  19. Pendulums • Simple pendulum:

  20. Pendulums • Physical pendulum:

  21. Chapter 13 Problem 28 How long should you make a simple pendulum so its period is (a) 200 ms, (b) 5.0 s, and (c) 2.0 min?

  22. Simple harmonic motion and uniform circular motion • Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the circular motion occurs

  23. Simple harmonic motion and uniform circular motion • Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the circular motion occurs

  24. Simple harmonic motion and uniform circular motion • Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the circular motion occurs

  25. Simple harmonic motion and uniform circular motion • Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the circular motion occurs

  26. Damping force Damping constant Damped simple harmonic motion

  27. Forced oscillations and resonance • Swinging without outside help – free oscillations • Swinging with outside help – forced oscillations • If ωd is a frequency of a driving force, then forced oscillations can be described by: • Resonance:

  28. Questions?

  29. Answers to the even-numbered problems Chapter 13 Problem 20 0.15 Hz; 6.7 s

  30. Answers to the even-numbered problems Chapter 13 Problem 38 65.8%; 76.4%

More Related