
When your classmates made a post in the forum

that was a calder action. He wants to see

examples of physics in real life, specifically

simple harmonic motion. So I came to the park

knowing that since simple harmonic motion is

everywhere I find some example here and here

I am in a tree. Turns out that when you displace a

tree branch just slightly from equilibrium and

release it, the resulting motion is simple harmonic

motion. Don’t believe me, I can prove it to you.

So, we’ve talked about simple harmonic motion,

we’ve talked about masses on springs and we’ve

talked about pendulums. Both of these when

displaced from their equilibrium will exhibit simple

harmonic motion and if we think that to why they

display simple harmonic motion, we remember

that it has something to do with some restoring

force being proportional to a displacement. So for

example for the mass on the spring, the restoring

force was equal to minus K times X. The K was

just a spring constant, X was the displacement

from equilibrium and the minus sign, well the

minus sign was very essential. The minus sign

told us that the force was always opposite the

displacement. So it tends to restore the mass to

its equilibrium. Now this is thinking in terms of

force. What about potential energy. Well for a

spring the potential energy was equal to one half

K times the displacement square and it’s this

term the displacement squared that I want to talk

about because we see that if we plot this,

potential energy versus displacement we get this

lovely parabola. Anything that has a parabolic

potential energy curve when plotted against some

sort of displacement will exhibit simple harmonic

motion. When it’s displaced away from this

equilibrium point, so if we can somehow show

that a branch fluttering back and forth somehow

exhibits this potential energy curve, well we’re

done. We’ve proven that, it must be simple

harmonic motion. Let’s see if we can do that.

Well let’s think, what could the potential energy

versus displacement look like for a branch and

here when I say displacement, let’s say positive X

means that the branch has been lifted up a little

bit and negative means it’s been pulled down a

little. To tell you the truth, I have no idea what this

curve looks like. I know that it’s hard to bend a

branch, so potential energy must somehow go up

as I increase displacement, in fact in either

direction. But then what does it do. Maybe there

is some sort of plateau in the energy curve, the

interpretation here would be, once we reach a

certain displacement it’s not any harder to

continue displacing the branch, to continue

pulling it further in further out. I don’t think this is

the case. Real branches don’t behave like that.

Maybe instead it actually gets really, really

difficult to continue bending the branch, or maybe

it’s somewhere in between, of course these

should be mirrored on this side. The fact is, we

just don’t know. The only way we could figure this

out, since branches are so complicated is by

doing an experiment. But I am going to make the

claim that we don’t need to because for small

displacements, look what we have here and they

can be proven mathematically in a very rigorous

way that for small displacements this trough must

has to be a parabola. So for this region, in here,

potential energy is equal to something times

displacement squared. And hell who really care

what that something is and in fact what we’ve

shown here is actually a deep truth of reality.

Anything with some equilibrium position whether

it’s a branch or a ball in a well or a mass on a

spring for small displacements will with absolute

certainty undergo a simple harmonic motion.

So on oscillating tree branch, that’s my

example of physics in action, what’s your's.