17. Periodic Motion

Energy in Simple Harmonic Motion

# Example

Patrick Ford

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Hey, guys, let's take a look at this. We're not giving any numbers, and this problem is all gonna be conceptual, right? So we're saying that we're increasing the amplitude of oscillation and were asked which of these statements are correct? So let's just take a look at the first one. The first one, the period of oscillation increases. Okay, so let me just go into my equations and figure out What do I have for equations of period? Well, that's going to be the big Omega equation right here. So in this equation for Omega and T and all that stuff, is there anything that involves amplitude? No, there's not right. It's just the frequency. The period and then K doesn't change with a and the cases of property. And then masses just mass. So that means the period of oscillation does not increase. So that's wrong. So let's take a look at Yeah, so that's wrong. Um, so let's take a look at the second one. The maximum acceleration increases. Let's look at our formulas for a max. We've got two of them. This one, a max is when, uh, K over M times A. So what happens is that in this equation for a Max? If k over M times A. If this a increases and K and M are just properties of spring and the mass of the object, then that means that a max also has to increase. So that means that this is actually a correct statement. I think I've got a repeat between C and D, but whatever. Okay, so that is actually true s all right that there Part C is asking for the maximum speed. So what happens to the maximum speed if we increase the amplitude? So just like we did over here, the V max is what they're looking for. So with this V, Max is equal to eight times omega. So we've got that V. Max is a Omega. Now let's see what happens if I increase this amplitude. Does anything happen to omega? Well, Omega is equal to just you know, all of this stuff over here, and we said that that doesn't change with amplitude. So if a goes up, what happens is the max goes up. Sometimes you have to check if one of these variables will, like decrease if you increase the amplitude because sometimes there might be that kind of relationship. So that's just like an extra question we have to ask. Okay, so that means that that is actually true, right? So the V Max does actually increase, So that is good. So what about this? This d which I guess we'll call the maximum kinetic energy. So Okay, Max. So let's look at our energy conservation equation. Well, so energy conservation is like the maximum elastic potential energy, whereas this is the maximum kinetic energy. So KMAX is when one half v max squared. So we just said that V max squared increases if you increase the amplitude. So that means that KMAX also has to increase. So that means Yes, it does. So sometimes you also might have those, like, indirect relationships as well, so that means that does increase. So what about the max potential energy? Okay, what does that mean? So again, we're gonna look at that same equation. We said that the maximum potential energy theological potential was one half k k squared. So for E, we've got that you Max is equal to once. We've got one half k a squared, so it's pretty obvious that if this a just goes up, that means the maximum potential energy also has to increase. So that means that that is true. Okay. And now for this last one, the maximum total energy. So maximum total energy is just gonna be this whole entire, um, mechanical energy formula. So what happens is again if you increase the maximum amplitude, right, If it goes up, then the whole entire mechanical energy goes up. So if mechanical energy is one half k a squared and a goes up, that means mechanical energy also goes up. So that means that that is also a true statement. Boom books. All right, so let me know if you guys have any questions about this and let's keep going.

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