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Resonance

Resonance. Lecture 32 November 21, 2008. Robert Hooke. “ ceiiinosssttuv ” Anagram for “ ut tensio , sic vis ” “as the extension, so the force”. Workbook Problems due Friday. Problems 14-1 through 8, pages 14-1 -- 5. Energy in Simple Harmonic Motion. Pendulum. Point mass on a string.

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Resonance

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  1. Resonance Lecture 32 November 21, 2008

  2. Robert Hooke • “ceiiinosssttuv” • Anagram for “uttensio, sic vis” • “as the extension, so the force”

  3. Workbook Problems due Friday • Problems 14-1 through 8, pages 14-1 -- 5

  4. Energy in Simple Harmonic Motion

  5. Pendulum Point mass on a string

  6. Physical Pendulum d L Center of gravity θ

  7. Damped Harmonic Motion Friction rears its ugly head!

  8. Damped Harmonic Motion

  9. Problem 14.15 A) When the displacement of a mass on a spring is ½A, what fraction of the mechanical energy is kinetic energy and what fraction is potential?

  10. B) At what displacement as a fraction of A, is the energy half kinetic and half potential?

  11. Problem 14.30 The center of gravity of a lower leg of a cadaver which had a mass of 5kg was located 18cm from the knee. When pivoted at the knee , the oscillation frequency was 1.6Hz. What is the moment of inertia of the lower leg?

  12. Problem 14.30

  13. Problem 14.33 • The amplitude of an oscillator decreases to 36.8% of it initial value in 10.0s. What is the time constant?

  14. Problem 14.33

  15. The period of this oscillator is approximately

  16. The period of the oscillator is • 1s • 2s • 5s • 10s

  17. The is zero at t = ?? approximately

  18. The velocity is zero when t = • 1.25 s • 2.60 s • 5.2s • 0.0 s

  19. The acceleration is a maximum when t = ??

  20. The acceleration is max when t= • 0.00s • 1.25 s • 4.0 s • None of the above

  21. The velocity is a maximum for t = ??

  22. The velocity is a maximum for t = • 0.0s • 1.25s • 2.6s • 4.0s

  23. Problem 14. 37 • A 25 kg child sits on a 2.0m long rope swing. To maximize the amplitude of the swinging, how much time should be between pushes?

  24. Problem 14.37

  25. Problem 14.32 A thin, circular hoop with a radius of 0.22m is hanging from its rim on a nail. When pulled to one side and released, the hoop swings back and forth. The moment of inertia for a hoop with the axis passing through the circumference is I = 2MR2. What is the period of oscillation?

  26. Problem 14.32

  27. Exam IV Wednesday, December 3 Chapter 10 and 14 Quick Review Monday

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