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Resonance Lecture 32 November 21, 2008

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Robert Hooke “ceiiinosssttuv” Anagram for “ut tensio, sic vis” “as the extension, so the force”

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

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Energy in Simple Harmonic Motion

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Pendulum Point mass on a string

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Physical Pendulum θ Center of gravityL d

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Damped Harmonic Motion Friction rears its ugly head!

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Damped Harmonic Motion

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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?

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

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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?

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Problem 14.30

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

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Problem 14.33

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The period of this oscillator is approximately

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The period of the oscillator is 1.1s 2.2s 3.5s 4.10s

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The is zero at t = ?? approximately

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The velocity is zero when t = 1.1.25 s 2.2.60 s 3.5.2s 4.0.0 s

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The acceleration is a maximum when t = ??

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The acceleration is max when t= 1.0.00s 2.1.25 s 3.4.0 s 4.None of the above

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The velocity is a maximum for t = ??

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The velocity is a maximum for t = 1.0.0s 2.1.25s 3.2.6s 4.4.0s

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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?

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Problem 14.37

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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 = 2MR 2. What is the period of oscillation?

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Problem 14.32

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

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