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

1. Title:
   10x-01 Physics in Action
2. Description:

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   When your classmates made a post in the forum
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   that was a calder action. He wants to see
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   examples of physics in real life, specifically
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   simple harmonic motion. So I came to the park
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   knowing that since simple harmonic motion is
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   everywhere I find some example here and here
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   I am in a tree. Turns out that when you displace a
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    tree branch just slightly from equilibrium and
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    release it, the resulting motion is simple harmonic
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    motion. Don’t believe me, I can prove it to you.
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    So, we’ve talked about simple harmonic motion,
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    we’ve talked about masses on springs and we’ve
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    talked about pendulums. Both of these when
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    displaced from their equilibrium will exhibit simple
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    harmonic motion and if we think that to why they
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    display simple harmonic motion, we remember
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    that it has something to do with some restoring
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    force being proportional to a displacement. So for
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    example for the mass on the spring, the restoring
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    force was equal to minus K times X. The K was
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    just a spring constant, X was the displacement
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    from equilibrium and the minus sign, well the
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    minus sign was very essential. The minus sign
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    told us that the force was always opposite the
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    displacement. So it tends to restore the mass to
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    its equilibrium. Now this is thinking in terms of
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    force. What about potential energy. Well for a
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    spring the potential energy was equal to one half
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    K times the displacement square and it’s this
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    term the displacement squared that I want to talk
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    about because we see that if we plot this,
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    potential energy versus displacement we get this
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    lovely parabola. Anything that has a parabolic
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    potential energy curve when plotted against some
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    sort of displacement will exhibit simple harmonic
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    motion. When it’s displaced away from this
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    equilibrium point, so if we can somehow show
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    that a branch fluttering back and forth somehow
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    exhibits this potential energy curve, well we’re
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    done. We’ve proven that, it must be simple
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    harmonic motion. Let’s see if we can do that.
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    Well let’s think, what could the potential energy
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    versus displacement look like for a branch and
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    here when I say displacement, let’s say positive X
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    means that the branch has been lifted up a little
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    bit and negative means it’s been pulled down a
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    little. To tell you the truth, I have no idea what this
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    curve looks like. I know that it’s hard to bend a
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    branch, so potential energy must somehow go up
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    as I increase displacement, in fact in either
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    direction. But then what does it do. Maybe there
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    is some sort of plateau in the energy curve, the
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    interpretation here would be, once we reach a
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    certain displacement it’s not any harder to
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    continue displacing the branch, to continue
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    pulling it further in further out. I don’t think this is
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    the case. Real branches don’t behave like that.
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    Maybe instead it actually gets really, really
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    difficult to continue bending the branch, or maybe
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    it’s somewhere in between, of course these
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    should be mirrored on this side. The fact is, we
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    just don’t know. The only way we could figure this
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    out, since branches are so complicated is by
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    doing an experiment. But I am going to make the
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    claim that we don’t need to because for small
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    displacements, look what we have here and they
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    can be proven mathematically in a very rigorous
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    way that for small displacements this trough must
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    has to be a parabola. So for this region, in here,
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    potential energy is equal to something times
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    displacement squared. And hell who really care
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    what that something is and in fact what we’ve
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    shown here is actually a deep truth of reality.
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    Anything with some equilibrium position whether
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    it’s a branch or a ball in a well or a mass on a
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    spring for small displacements will with absolute
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    certainty undergo a simple harmonic motion.
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    So on oscillating tree branch, that’s my
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    example of physics in action, what’s your's.