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← 07-28 So What?

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

  1. Now you're maybe asking yourself, so what? Who cares about this phase diagram?
  2. You're in for a treat. Notice that when I pick out a point on this circle.
  3. And remember this circle tells us all the locations in what we can call phase space
  4. which is a combination of position in velocity.
  5. All the locations in phase space where we might find this object. Let's look at this point for example.
  6. Well, this point corresponds to a position down here and to a velocity over here.
  7. Well, I'm seeing something very fascinating right now.
  8. Let's just draw a line from the center over to here.
  9. Let's draw a line from the center out to the point we're talking about.
  10. Oh, I think you're seeing it too now. Well, check it out.
  11. This point has an angle associated with it. I'm going to call that angle θ.
  12. It has an opposite side and the length of this opposite side
  13. well that corresponds to this length over here same as the velocity, V/Vmax.
  14. And this triangle has an adjacent side and this adjacent side corresponds to
  15. the position of the particle or the block at this instant in time.
  16. Another great thing is that since we've chosen to write the speeds and positions
  17. this ratios of X/Xmax and V/Vmax this circle has radius 1.
  18. The hypotenuse is just 1. That's such an easy number to deal with.
  19. Now, can you figure out a very important equation namely what trigonometric function
  20. goes here and which goes here?
  21. I'll give you a hint. It's either sine, cosine, or tangent. And it's either sine, cosine, or tangent.
  22. So is X/Xmax the sin θ? The tan θ? Cos? Fill in your answers here and here.