Simply being kim3/13/2023 ![]() Why should I care about that? You should care about that because these satisfy some very special rules that I'll show you throughout this video and it turns out that even though this doesn't sound very simple, they are much simpler than the alternative of Non-Simple Harmonic Oscillators. And you still might not be impressed, you might be like who cares if the restoring force is proportional If that's the case, then you've got what we call a Simple Harmonic Oscillator. If I pulled this pendulum back with two times the angle, I'd get two times the restoring force. Three times as much, I'd get three times the restoring force. To the displacement, if I pulled this mass back twice as much, I'd get twice the restoring force. Will be a restoring force, but if it's proportional So what that means is if I pull this mass to the right there Have a restoring force that's proportional to theĪmount of displacement. So what makes Simple Harmonic Oscillator's so special is that even though all oscillators have a restoring force, Simple Harmonic Oscillators But they're something called the Simple Harmonic Oscillator. And you might be thinking, that's a pretty dumb name because that doesn't sound very simple. We call them Simple Harmonic Oscillators. Now there's lots of oscillators, but only some of those oscillators are really special, and we That's what we mean by a restoring force. It back to the right, always trying to restore this mass back to the equilibrium position. But if I pull the mass to the left, gravity tries to pull If I pull the pendulum to the right, gravity is the restoring force trying to bring it back to the left. It tries to restoreĪlways, it tries to restore mass back to the equilibrium position. And if I pull the mass right, the spring pulls left. To the equilibrium position, we're trying to push it back there. ![]() If I push this mass to the left, the spring's like uh uh, we're movin' this thing back However, if I pull this mass to the right, the spring's like uh uh, now I'm gonna try and restore this mass back to the equilibrium position, the spring would pull to the left. In other words, if you just sat the mass there it would just stay there because there's no net force on it. Mass would be 0 because that's what we mean by So for instance, for this mass, if this mass on the spring was sitting at the equilibrium position, the net force on that So every oscillator hasĪn equilibrium position, and that would be the point at which there's no net force on the Like the name suggests, tries to restore this system, but restore it to what? Restore the system to Share this common fact, that they all have a restoring force. So you could ask why do these things oscillate in the first place, and it's because they all Masses on springs, pendulum, but there's many other examples and all those examples share one common feature of why they're an oscillator. Going back and forth, that's an oscillator. Mass connected to a string, and you pull the mass back and then it swings back and forth. Or another common example is a pendulum, and a pendulum is just a Pull this mass back, it's gonna oscillate back and forth, and that's what we mean by an oscillator. So for instance, a mass on a spring here is an oscillator if we And what an oscillator is is an object or variable that can move back and forth or increase and decrease, go up and down, left and right, over and over and over.
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