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.