## ← 10x-01 Physics in Action

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Showing Revision 1 created 11/04/2012 by podsinprint_user1.

2. that was a calder action. He wants to see
3. examples of physics in real life, specifically
4. simple harmonic motion. So I came to the park
5. knowing that since simple harmonic motion is
6. everywhere I find some example here and here
7. I am in a tree. Turns out that when you displace a
8. tree branch just slightly from equilibrium and
9. release it, the resulting motion is simple harmonic
10. motion. Don’t believe me, I can prove it to you.
11. So, we’ve talked about simple harmonic motion,
12. we’ve talked about masses on springs and we’ve
13. talked about pendulums. Both of these when
14. displaced from their equilibrium will exhibit simple
15. harmonic motion and if we think that to why they
16. display simple harmonic motion, we remember
17. that it has something to do with some restoring
18. force being proportional to a displacement. So for
19. example for the mass on the spring, the restoring
20. force was equal to minus K times X. The K was
21. just a spring constant, X was the displacement
22. from equilibrium and the minus sign, well the
23. minus sign was very essential. The minus sign
24. told us that the force was always opposite the
25. displacement. So it tends to restore the mass to
26. its equilibrium. Now this is thinking in terms of
27. force. What about potential energy. Well for a
28. spring the potential energy was equal to one half
29. K times the displacement square and it’s this
30. term the displacement squared that I want to talk
31. about because we see that if we plot this,
32. potential energy versus displacement we get this
33. lovely parabola. Anything that has a parabolic
34. potential energy curve when plotted against some
35. sort of displacement will exhibit simple harmonic
36. motion. When it’s displaced away from this
37. equilibrium point, so if we can somehow show
38. that a branch fluttering back and forth somehow
39. exhibits this potential energy curve, well we’re
40. done. We’ve proven that, it must be simple
41. harmonic motion. Let’s see if we can do that.
42. Well let’s think, what could the potential energy
43. versus displacement look like for a branch and
44. here when I say displacement, let’s say positive X
45. means that the branch has been lifted up a little
46. bit and negative means it’s been pulled down a
47. little. To tell you the truth, I have no idea what this
48. curve looks like. I know that it’s hard to bend a
49. branch, so potential energy must somehow go up
50. as I increase displacement, in fact in either
51. direction. But then what does it do. Maybe there
52. is some sort of plateau in the energy curve, the
53. interpretation here would be, once we reach a
54. certain displacement it’s not any harder to
55. continue displacing the branch, to continue
56. pulling it further in further out. I don’t think this is
57. the case. Real branches don’t behave like that.
58. Maybe instead it actually gets really, really
59. difficult to continue bending the branch, or maybe
60. it’s somewhere in between, of course these
61. should be mirrored on this side. The fact is, we
62. just don’t know. The only way we could figure this
63. out, since branches are so complicated is by
64. doing an experiment. But I am going to make the
65. claim that we don’t need to because for small
66. displacements, look what we have here and they
67. can be proven mathematically in a very rigorous
68. way that for small displacements this trough must
69. has to be a parabola. So for this region, in here,
70. potential energy is equal to something times
71. displacement squared. And hell who really care
72. what that something is and in fact what we’ve
73. shown here is actually a deep truth of reality.
74. Anything with some equilibrium position whether
75. it’s a branch or a ball in a well or a mass on a
76. spring for small displacements will with absolute
77. certainty undergo a simple harmonic motion.
78. So on oscillating tree branch, that’s my
79. example of physics in action, what’s your's.