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The diagram below shows snapshots of an oscillator at different times: What is the frequency of the oscillation? (0.0 $ (=0.30 [70.45 $ {=0.90 $ (1.,35 $ [=1.80 $~0...

Question

The diagram below shows snapshots of an oscillator at different times: What is the frequency of the oscillation? (0.0 $ (=0.30 [70.45 $ {=0.90 $ (1.,35 $ [=1.80 $~0.10 m --0.10 m(Unit = Hz)

The diagram below shows snapshots of an oscillator at different times: What is the frequency of the oscillation? (0.0 $ (=0.30 [70.45 $ {=0.90 $ (1.,35 $ [=1.80 $ ~0.10 m - -0.10 m (Unit = Hz)



Answers

Draw a graph showing the position-versus-time curve for a simple harmonic oscillator (a) with twice the frequency of that shown in Figure $P 10.5$ and (b) with the same frequency but twice the amplitude as shown in the figure.

So for this question, basically what we're asked to do is to see to modified frequency and amplitude and see how those two variables changes in those two variables can without on the graph. So here we have the original graph that we're gonna bother five based on and I'll grab. You can see that the original, um, time period, T IHS. I'm here to here, so and it's gonna be a point for second have been very t close to 14 seconds. And we can also see that aptitude this here. So we're gonna say a close to to. So since we have the original crab eaters here, now we can take a look at a MP and see what we can do to change on the graph. So in question A, um, we need to find the frequency. And since we know that t because 2.4 seconds now we can clogging the equation. Ash, you close to one over tea and hook 14 So convincing. One over point for will give us the frequency off 2.5 hertz. So, um, this is different. Quincy, 25 hertz. This the original frequency that's call it off. Not the original frequency on on the graph. And now, since the question is asking us to graph, uh um graph. Ah, Austin. Either That has twice the frequency eschewing autograph. We knew too. Multiply Have not. So that's kind f Hey, is, um it's a new F. It is twice the old frequency have not. So it is twice 2.5. We shall give us five hertz and the new period. T would also change plays down the FAA. So Greece A t a you close to a one over half a, you will give us one know very five hertz, and we'll get 0.2 seconds. So if we go back to the graph, um, are amplitude wouldn't change just by the frequency, But, um, we're gonna have a shorter T. So it's now ISS. It's, um, points two sevens comparing 2.4 this graph, its basic on a shrink horizontally. So if we tried in New York, where I found the original wonder, it's gonna be like this. Oops. It's got a vicious streak again. According to go down like this, that's gonna be new brush for part A. Okay, so now we're gonna be moving into part B, and then you raise off the calculations and here, so we have more room to do. Part B. Um, so part b of the problem is asking us about, um, how the changing amplitude would Rick slapped on a graph? So pretty much we have to sing. Um, t. But the A be changed from two two centimeters, too. Four centimeters. So we're gonna see all part B. They be would be force and meters because it's twice the original amplitude. And, um, this one is pretty easy. We don't even do any calculation. We're just gonna expand it, um, on the wire access direction. So if Majaida graph out like this, it's going to start from four instead of two on the original one. And but the horizontal Alsace is would still be the suit. So 0.1 12 and one Syrian point for, So it's gonna start from four. It was down to one, 23 and Bridges goes back to the original decision at 0.4. So you can see there. How is this stretched? Um vertically comparing to the original graph

So here we're gonna relate essentially Hook's law to force of gravity. And so here the equilibrium point is the point where the mass would hang at rest, where gravitational force of course, equals M g. And then we know this. The spring is stretched delta y Equalling 10 centimeters where we can say 0.10 meters. And so this is the force of the spring from Hook's Law would be k doubts or why so we can say then that que delta y equaling MGI Essentially then, okay, over m equals G over Don't. So why This is equaling 9.8 meters per second squared, divided by 0.10 meters, giving us 98 seconds 98 per second squared. And so the ratio is what we need to find. The fruit is where we need to use to find the frequency so the frequency would be equaling. 21 over two pi multiply buzz for a root of K over em. This is equaling 1/2 pi most played by the square root of 98 seconds to negative second, and this giving us 1.58 hurts. That is the end of the solution. Thank you for watching

In this case, we have to show that the angular frequency of those licenses Omega is equals. Two squared of, uh, Kevin Douglas Kato, divided by m here. This K one is the spring constant of the spring one. And the K two is the spring constant of the spring two for the given case. When the mess is attached with two different springs, we can wipe the dynamics of this, uh, this this system as Emma's equals two. Yeah, Emma is equals two minus into K one plus K two into X. So we can white. The exploration as a Z equals two minus into K one, plus K two, divided by m in two X at school required number one for the simple harmonic motion we can white as equals two minus omega squared X. And this will be our equally number two are using equation number one and number two. We can write the expression for this omega squared as omega squared is equal to okay. One plus care to divided by m. So from here we can write the expression for this omega omega is equals to square out of kill one plus K two divided by and so this is a required relationship. Thank you

Hello everyone. We will be discussing dimensions in this recording. So before we continue we should know that the dimension of time is capital D. Good records. And may I say it's capital m capital um in square brackets as well. No, since frequency is in most of time and estimations should be b minus one or inverse of T. We have the equation F equals CMkellystar rex multiple advocated broadway where C is dimensional list? Well it is a constant uh matches Emma's obviously mess and it's the universe will be kg. But the dimension that the units of k here is a kilogram per second squared. Let's put our dimensions, no equation one, it comes mm most equals um our X. Okay, um Our way. Mhm. Ar minus do I? Now? We will be comparing mass and time on both sides. So we will be getting two equations from this. Let's compare messes. It becomes X plus Y equals zero because there is no mess on this side. And in question we will get as minus one equals minus two Y. Unless it's all by our question, our second question here, we will get why equals minus one by minus two or one by two. Let's put this this value in our first equation here, X becomes minus way mm This implies minus 1/2 and we have to put these values of X and Y values in our equation one we have F equals C. M. To the power minus 1/2. Multiply by gay to the power one or two are in the words we have F equals C. A. Or him. Oops. This this morning. Yeah. Hole in the road. That's it.


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