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$\bullet$ $\bullet$ A mass $m$ is attached to a spring of force constant 75 $\mathrm{N} / \mathrm{m}$ and allowed to oscillate. Figure 11.38 shows a graph of its velocity $v_{x}$ as a function of time $t .$ Find (a) the period, (b) the frequency, and (c) the angular frequency of this motion. (d) What is the amplitude (in $\mathrm{cm} )$ , and at what times does the mass reach this position? (e) Find the maximum acceleration of the mass and the times at which it occurs. (f) What is the mass $m$ ?

a) 1.6 $\mathrm{s}$b) 0.625 $\mathrm{Hz}$c) 3.93 $\mathrm{rad} / \mathrm{s}$d) 5.1 $\mathrm{cm}$ t=0.2s,1.4s,2.0se)79 $\mathrm{cm} / \mathrm{s}^{2}$ f)4.86 $\mathrm{kg}$

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Winnipeg

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Alright, guys. So let's take a take. A look at the first question. The first question was asking us What is the time, period? But chronograph in town. The time periods 1.6 2nd Okay. Questions he was asking us What is the frequents? Frequency is equal to one over time here, which is walrus. He which will give us 1/1 10.6 seconds, which is 0.625 hers. All the pregnancy. Now we know the frequency so can determine the ankle of purpose. The anger progress is just equal to to buy up, which will give us two pi times your opponent six to buy hers, which is equal to 3.93 radium per second. Question D was asking us what is the Amber to? And also at what time you, uh, you reach the aptitude? Well, when the objects When the all station Christie empathy, the speed will be zero. So phonograph wins. How? That and 0.2 2nd one point force happened in two seconds. Those points and with zero speak. Okay, So see, so they are in general being them is that in the maximum displacement they can get, which is the MP to position. Okay, so the answer four times is 0.2 2nd 1.4 seconds to second. And well, now in to determine the value for the entity. How come you determine about 20 MPA too? Well, nearly. You know, the match mints B is equal to empty two times angular frequency. So which means that MPT is equal to Maximus. Be divided by angry frequency. And we have the next month. Well, I'll see, which is 27 centimeters per second and the Omega watches. Angular frequency is 3.93 Radio second, and this will give us the empty is able to 20 centimeter for second square. I'm sorry, Tony. Senate, Centimeter per second. You have Ah, three point. Naturally radiant. Per second. This will give us the empty was about 5.17 Here it is. Junk. Till next question. So in expression was asking us what is the maximum acceleration? While the maximum acceleration is equal to the institute times, the angular frequency square the front of previous question with only empathy. School too. One point warrant. Centimeter and angular frequency is equal to 3.93 reading per second. So this will give us a maximum Acceleration is equal to 5.1 centimeter times 3.93 rating her second the whole thing square. So the maximum accelerated. So a maximum acceleration is equal to 79 centimeter for a second square. Okay, if the last question I was asking us what is the mass of the object so? Well, we know the force Constant is equal to master. Oh, my guesswork And all my guys, the ankle purpose we know anger frequency is 3.93 radium per second. Okay, so if we do some arrangement here, we've got masses just simply able to force constant over omega squared. So this will give us Emory School to 75. No, Tom per meter overall. Make us where we just 3.93 radiant per second and the whole thing square. This would be arrested mass off the item on the mass. Such object is equal to 12 point a six kilograms J. And that's the answer for this question. Thank you.

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