# Harmonic Oscillator Solution: Check:

## Presentation on theme: "Harmonic Oscillator Solution: Check:"— Presentation transcript:

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

Use Mathematica (plot_cosine.nb file)
Notice period: a) Is the right answer; the slope is constant.

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.

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

Harmonic oscillators everywhere! Pendulum
a) Is the right answer; the slope is constant.

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

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

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

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

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

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

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

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

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

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

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

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?