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← 07-58 Finding Simple Harmonic Motion

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Showing Revision 1 created 07/23/2012 by Amara Bot.

  1. Okay, let's see. We want a period of 1 second.
  2. Let's convert this to an angular frequency ω using this equation.
  3. So, we want an angular frequency of 2π, an I know that ω²
  4. is equal to whatever this thing is, the minus something times x.
  5. In this case, ω² is equal to g/L. Let's solve this for L.
  6. This gives me a length of 0.25 meters.
  7. Now, it turns out that for pendulum clocks, actually, we might want a period of 2 seconds.
  8. The reason is because let's say we had a pendulum with a period of 1 second.
  9. That means that it takes 1 second for when I pull it back to go
  10. over here and then all the way back.
  11. That's actually quite a bit of motion and a period of 2 seconds is actually a little bit better,
  12. because then every time the pendulum reaches one if its extrema,
  13. either all the way over here or all the way over there,
  14. we know 1 second has passed--half of the period.
  15. I wonder what would be the period for a 2-second pendulum.
  16. Why don't ask Tjeerd the clockmaker what he thinks.
  17. [Tjeerd ] When you design a pendulum or pendulum clock,
  18. the thing that mostly influences the period of oscillation is the length of the your pendulum.
  19. If you have an ideal pendulum, a fictional pendulum,
  20. made out of no materials as a mathematical piece,
  21. the pendulum of a second, oscillating in a second,
  22. will have a length of about a meter.
  23. A pendulum is made out of materials, and the rod, for instance, is made out of steel or brass,
  24. which brings the center of oscillation up.
  25. That's why you need a heavy pendulum bulb underneath the pendulum--
  26. to bring the center of gravity in the pendulum down
  27. to have your proper theoretical length.