Simple Harmonic Oscillator

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© 1998-2008 by Glenn Elert -- A Work in Progress
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Discussion

Trust me. It's simple.

a b c d

Summary

• bullet

Problems

practice

1. Write something.
   • Answer it.
2. Write something else.
   • Answer it.
3. Write something different.
   • Answer it.
4. Write something completely different.
   • Answer it.

conceptual

1. Given an object oscillating horizontally in simple harmonic motion, where in the course of its motion are the magnitudes of the following quantities equal to zero? Where are they equal to their maximum value?
   1. acceleration
   2. elastic potential energy
   3. kinetic energy
   4. net force
   5. speed
2. Given an object oscillating horizontally in simple harmonic motion, which graph of energy vs. displacement shown below … best represents …
   1. the total energy of the object-spring system?
   2. the kinetic energy of the object?
   3. the potential energy of the spring?
   Explain your reasoning.

numerical

1. A 1.0 kg cube oscillates horizontally on the end of a spring like the one shown below. The extreme displacement of the mass as it oscillates is 0.10 m and its period of oscillation is 0.50 s.
   1. Determine the spring constant.
   2. After 27 periods, the cube comes to rest. Determine the energy dissipated by friction.

statistical

1. A group of students set up an inertial balance, loaded it with various known masses, set it oscillating, and measured the corresponding periods. Then they repeated the experiment with a series of items of unknown mass (basically, whatever they brought with them to lab that day).
   1. inertial-balance-calibration.txt
      Derive an equation that relates mass to period for this inertial balance using the measurements taken in the first half of the experiment.
   2. inertial-balance-unknowns.txt
      Apply the equation you just derived to the measurements taken in the second half of this experiment and determine the masses of the objects that the students brought with them to lab.
   3. This balance consisted of a small lab cart placed on a horizontal track with two identical springs mounted on opposite ends. Determine …
      1. the mass of the empty balance (the mass of the small lab cart) and …
      2. the spring constant of the two springs. (Be careful with the units here. The masses were recorded in grams, but the spring constant should be stated in N/m and the newton is based on the kilogram.)

Resources

• general
  • The Mechanical Universe and Beyond (video on demand, login required)
    • Harmonic Motion, The music and mathematics of periodic motion.
• inertial balance
  • Cornell's Tiny, Vibrating Paddle Oscillator Senses the Mass of a Virus, Bill Steele, Cornell University
• video clips
  • human slingshot
    • clip 1
    • clip 2

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