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**Harmonic Oscillator Solution: Check:**

a) Is the right answer; the slope is constant. Check:

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**Use Mathematica (plot_cosine.nb file)**

Notice period: a) Is the right answer; the slope is constant.

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**Take x=0 at equilibrium and equations work out identically **

as for the horizontal spring: Solution: a) Is the right answer; the slope is constant.

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Energy: a) Is the right answer; the slope is constant.

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**Harmonic oscillators everywhere! Pendulum**

a) Is the right answer; the slope is constant.

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**Harmonic oscillators everywhere!**

Attraction between atoms in a molecule Level in connecting vessels A floating bob a) Is the right answer; the slope is constant. The charge in an LC circuit

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**If you double the amplitude of a harmonic oscillator, the oscillator’s period**

Decreases by 2 Decreases by √2 Does not change Increases by √2 Increases by 2

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**If you double the amplitude of a harmonic oscillator, the oscillator’s period**

Decreases by 2 Decreases by √2 Does not change Increases by √2 Increases by 2

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**If you double the amplitude of a harmonic oscillator, the maximum speed**

Decreases by 2 Decreases by √2 Does not change Increases by √2 Increases by 2

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**If you double the amplitude of a harmonic oscillator, the maximum speed**

Decreases by 2 Decreases by √2 Does not change Increases by √2 Increases by 2

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**If you double the spring constant of a harmonic oscillator, the oscillation frequency:**

Decreases by 2 Decreases by √2 Does not change Increases by √2 Increases by 2

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**If you double the spring constant of a harmonic oscillator, the oscillation frequency:**

Decreases by 2 Decreases by √2 Does not change Increases by √2 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? Approx 0.5 sec Approx 1 sec Approx 4 sec Approx 10 sec 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? Approx 0.5 sec Approx 1 sec Approx 4 sec Approx 10 sec Approx 40 sec

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**How do you measure the mass of an astronaut in orbit**

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? Approx 20 kg Approx 40 kg Approx 60 kg Approx 80 kg None of the other options

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**How do you measure the mass of an astronaut in orbit**

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? Approx 20 kg Approx 40 kg Approx 60 kg Approx 80 kg 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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1 P1X: Optics, Waves and Lasers Lectures, 2005-06. Lecture 2: Introduction to wave theory (II) Phase velocity: is the same as speed of wave: o Phase velocity:

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