Intuitive Explanation of Resonance by Helmholtz

Okay, so it's Hey, it's like a pendulum Pendulum does this Has anyone seen the resonance already? Yeah Was there resonance already was the effect of resonance already on display with what I did so far Yes, there was so let's let's Walk through it. So if I did this no resonance, right? I Activated the natural frequency the only frequency I can activate through initial displacement No resonance there Okay, but I but that's not what I did. I did this So there was a little bit of a drive, right? I started doing this Now let's talk about what did I do on the intuitive level? Here's what I did. I pulled it to the left and The moment I pulled it to the left. It was trailing a little bit, right? So then it's one to the right I'm sorry Mixing up left and right so your left and your right. So first I pulled it to the right And so then it's one to the right and at the moment where it was most just of the greatest displacement I pulled it a little bit to the left and at that point I artificially increased the amplitude Let's see because initially I pulled it like this so if you see it's a small amplitude so it's one back According to its amplitude and it just that right moment. The timing was paramount. I pulled it to the left a little bit and do you see how Now the amplitude was artificially increased because I just displaced the base and so it swung back and at this exact moment I pulled it to the right again and therefore increase the amplitude again And so now it has greater amplitude so that And all of us are very good at this So that is resonance Because I matched the frequency of my drive It is very fundamental What is very fundamental that the amount of time that it takes to reach? The highest point the greatest displacement is the same regardless of the amplitude So whether it oscillates just a little bit one two Three that's the frequency now. Let me give it this displacement one two Three right the exact same period as long as the amplitude is small when you do this It's changes when it's big one Two, I think it's slower, right? Maybe there's also stretch No, it's more than that It's only for very very small amplitudes Not very small you define what small is the more the smaller it is the more accurate the statement, but for smaller amplitudes Relatively small amplitudes the period is relatively constant. That's the basis of all the pendulum based clocks that Period does not depend on amplitude But if the amplitude is larger than the period changes and I can't resist Telling you about this amazing result by the incredible Dutch mathematician whose name I cannot learn to pronounce fugitives Contemporary of Newton probably a couple years older than Newton Permanent with great contributions to calculus, but he also wanted to solve the problem of the fact that the Period of a pendulum does depend on its frequent on its amplitude a little bit Actually, it's a fascinating question to answer why it doesn't for small amplitudes. What's going on there on an intuitive level? I think we know the math Intuitive levels what goes on there? So he made the following invention. He said let's give it some shape I've never studied this so maybe before I post the video, I'll Double-check this I said do it could make a pendulum do this Oscillate in a space like this and then follow the curve like this. So as it As it oscillates it constantly changes its length And you figured out what this shape needs to be In order for the period to not depend on the amplitude at all So if it's tiny it just does kind of does this but when it's very large it does this So you figured out what this shape would need to be and it was a cycloid shape that a point traces when a wheel rolls But where were we so let's get back to this so The period does not depend on the amplitude. So my Adjustments that I was talking about We're all at equal times and so my drive at a frequency and What frequency does it have? Well precisely the natural frequency of this body So I think that this is I found this explanation in Elmholtz book So I think that this gives you perfect intuition for how resonance does its job And I just want to repeat one more time that it's remarkable that There's quite a bit of complexity. Yes. This was a very simple explanation, but when it comes to bridges and voice and all of those other phenomena They're pretty complicated, but they have this very very simple mathematics at the cross Okay, that's resonance another explanation