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Published byRickey Vercoe Modified about 1 year ago

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Harmonic Oscillator Solution: Check:

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Use Mathematica (plot_cosine.nb file) Notice period:

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Take x=0 at equilibrium and equations work out identically as for the horizontal spring: Solution:

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Energy:

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Harmonic oscillators everywhere!Pendulum

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Harmonic oscillators everywhere! Level in connecting vessels A floating bob Attraction between atoms in a molecule The charge in an LC circuit

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If you double the amplitude of a harmonic oscillator, the oscillator’s period A.Decreases by 2 B.Decreases by √2 C.Does not change D.Increases by √2 E.Increases by 2

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If you double the amplitude of a harmonic oscillator, the oscillator’s period A.Decreases by 2 B.Decreases by √2 C.Does not change D.Increases by √2 E.Increases by 2

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If you double the amplitude of a harmonic oscillator, the maximum speed A.Decreases by 2 B.Decreases by √2 C.Does not change D.Increases by √2 E.Increases by 2

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If you double the amplitude of a harmonic oscillator, the maximum speed A.Decreases by 2 B.Decreases by √2 C.Does not change D.Increases by √2 E.Increases by 2

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If you double the spring constant of a harmonic oscillator, the oscillation frequency: A.Decreases by 2 B.Decreases by √2 C.Does not change D.Increases by √2 E.Increases by 2

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If you double the spring constant of a harmonic oscillator, the oscillation frequency: A.Decreases by 2 B.Decreases by √2 C.Does not change D.Increases by √2 E.Increases by 2

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What will be the natural oscillation period of a 30-kg child on a swing whose seat is 3.2 m below the bar where the chains from the seat are attached? A.Approx 0.5 sec B.Approx 1 sec C.Approx 4 sec D.Approx 10 sec E.Approx 40 sec

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What will be the natural oscillation period of a 30-kg child on a swing whose seat is 3.2 m below the bar where the chains from the seat are attached? A.Approx 0.5 sec B.Approx 1 sec C.Approx 4 sec D.Approx 10 sec E.Approx 40 sec

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How do you measure the mass of an astronaut in orbit? NASA engineers designed a Body Mass Measuring Device. It is essentially a chair of mass m=20 kg mounted on a spring. (The other end is connected to the massive space station itself.) The period of oscillation of the empty chair is measured to be 1 s. When an astronaut is sitting in the chair, the period is 2 s. What is the mass of the astronaut? A.Approx 20 kg B.Approx 40 kg C.Approx 60 kg D.Approx 80 kg E.None of the other options

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How do you measure the mass of an astronaut in orbit? NASA engineers designed a Body Mass Measuring Device. It is essentially a chair of mass m=20 kg mounted on a spring. (The other end is connected to the massive space station itself.) The period of oscillation of the empty chair is measured to be 1 s. When an astronaut is sitting in the chair, the period is 2 s. What is the mass of the astronaut? A.Approx 20 kg B.Approx 40 kg C.Approx 60 kg D.Approx 80 kg E.None of the other options

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Known mobster and gambler Larry the Loser is found dead, hanging at about the 7-story level from a bungee cord tied to the top of the 15-story (45 m) Prudential Building in downtown Chicago. Larry has a mass of 90 kg and when the bungee cord is cut down, it is found to have a relaxed length of 5 stories. Detective Lestrade from the Chicago Police Department thinks that Larry must have been bungee-jumping from the top of the building and just unluckily hit the ground, but you know that Larry was murdered. What is your evidence?

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