A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. When the amplitude of the motion is 0.090 m, it takes the block 2.70 s to travel from x = 0.090 m to x = -0.090 m. If the amplitude is doubled, to 0.180 m, how long does it take the block to travel (a) from x = 0.180 m to x = -0.180 m?

Video transcript

Hey everyone in this problem, we have a plastic disc fixed to a perfect horizontal spring and placed on a horizontal smooth surface where it oscillates in simple harmonic motion. The mass travels from negative a. Too positive A in 3.42 seconds. Okay. And were asked what is the time taken to travel from negative or positive? A Over 22 negative 8/2. If the amplitude is halved to a over two. Okay. Alright. So we're traveling from negative A. Too positive A. Where the amplitude is a. Okay, so if we travel from negative a too positive A. Okay, this is a half period. I remember a full period is when we go from either negative a back to a negative A or a back to a K. We're getting back to the same point. Okay? So if you imagine we just draw um a little diagram. Okay, so we're gonna be at negative A. And then we're going to travel up to a, okay, so this is half a period. The full period would be to come either back down this way or come back up this way. Okay, so this is half a period. T over two. Yeah. Okay, and this tells us that T over two Is equal to 3. seconds. Okay, because it takes 3.42 seconds to travel that distance. Alright, well what equations do we have relating to T? We have the following that omega is equal to two pi f. Which is equal to two pi over T. Which is also equal to the square root of K. Over graham. Okay, alright, so we're gonna keep this in mind as we do the rest of the press. Now we're asked what the time taken to travel from positive A over 22 negative A over to when the amplitude is halved to a over two. Okay, well if the amplitude is a over two then traveling from positive A over 22, negative 8/2 is still going to be T over two. Okay, so travel from Positive a over two two. Negative over to when the amplitude is a over two. Okay, so you're going from the positive amplitude down to the negative amplitude, This is still over two. Okay, it's still half the period you're going from the maximum up to the minimum or in this case the minimum down to the maximum. Alright. Travel from able to when amplitude is able to is still T over two half a period. Now, when we change the amplitude does that period t change? Well, let's look at our equations. Okay, is not in these equations relating to the period T. Okay, so A is not. And these equations okay, which means that it doesn't actually affect the period. Okay, so changing the amplitude does not affect the period, which means that T over two when our amplitude is have 2/2 is still going to be equal to 3.42 seconds. Huh? Alright, so our answer here is d Okay, the time it takes to travel from positive over two to negative over to when the amplitude is have 2/2 is going to be the same as the time it takes to travel from negative a too positive A when the amplitude is a. Okay, so we have answered D. Here 3.42 seconds. That's it for this one. Thanks everyone for watching. See you in the next video.