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4-foot spring measures feet long after Mass weighing pounds attached to it: The medium through which the mass moves offers damping force numerically equal to times ...

Question

4-foot spring measures feet long after Mass weighing pounds attached to it: The medium through which the mass moves offers damping force numerically equal to times the instantaneous velocity- Find the equation of motion the mass is initially released from the equilibrium position with downward velocity of fts_ (Use 32 ft/s? for the acceleration due to gravity )x(t)Find the time at which the mass attains Its extreme displacement from the equillbrium position_What the position of the mass at this

4-foot spring measures feet long after Mass weighing pounds attached to it: The medium through which the mass moves offers damping force numerically equal to times the instantaneous velocity- Find the equation of motion the mass is initially released from the equilibrium position with downward velocity of fts_ (Use 32 ft/s? for the acceleration due to gravity ) x(t) Find the time at which the mass attains Its extreme displacement from the equillbrium position_ What the position of the mass at this Instant? The extreme displacement Is feet:



Answers

A 16 -lb weight is attached to the lower end of a coil spring suspended from the ceiling and having a spring constant of $11 \mathrm{lb} / \mathrm{ft}$ The resistance in the spring-mass system is numerically equal to the instantaneous velocity. At $t=0$ the weight is set in motion from a position 2 ft below its equilibrium position by giving it a downward velocity of $2 \mathrm{ft} / \mathrm{sec} .$ At the end of $\pi$ sec, determine whether the mass is above or below the equilibrium position and by what distance.

We have a £16 way. The way is £16 and we have a mass, which is about half half a slug. So we had and we have also a k a constant, which is £1.1 pound per fief. And so we started for the equation. Such ingenuity. Oh, yeah, And also, uh, the spring mass system. It's equal to the detention ations philosophies that have times X double time plus ex prime plus X equals zero. And another thing waas that since it's going to be below it's going down work. We assume that it's gonna be positives with X zero is equal to 2 ft and ex prime of cereals you 2 ft per second. So now we saw for it sold half times art were close are plus one is includes hero. So this equation whole equation is simply gonna view exit e. He can see won t of dynasty co sign P plus C to G of minus t sign of he x zero would be See you on people till and then we do ex prime of tea. Which is gonna be You may see one year my next heat co sign he May I see one? He it means, Do you have raised E minus two e a priest? He fine, he plus two. Do you have made Ex prime of zero would be equal to minus C one plus e t cling to it's see once you go to see two people for to the equation simply feet exit key calling two of e of minus tedx co sign P plus uh, for e f minus. He sign he and then for Harvey were doing. We saw her ex pie, which is equal. Teoh means to e of my spy, the community that it's a to 10 t of my high feet above, very above its equilibrium.

It's a question is £8 stretches a spring by 4 ft. Resistance offered to the motion of the spring is 1.5 times. The instantaneous velocity external force applied is six plus cities to minus T measuring pounds. Now, initial condition given is it is released 2 ft above the equilibrium. So that is what we have to remember. And the velocity is 3 ft per second downwards. Okay, so we need to find position after two seconds. So let's model the function. So it is given that M G is a pound. Therefore, m g R E M s 85 inches. 32. So m is one life for now, M G force stretches a single 4 ft, which causes restoring force on the spring and this to get balanced. They must because two k x mgs eight k. We don't know Texas for some case, too. Now, Delta is the resistance constant. So it is since the Resistance Force is giving us the times y rash studio Delta is one point. Wait, wait. Forget n f d a six plus minus t. It would be okay. So now we can solve this. So we have are the creationists and where the biggest Delta minus plus K y equals to 40 and M is one by four wide level s plus Delta. She's 1.5 wireless plus cages to is a culture of six. Plus it is minus d. Okay, so we can go obsolete. Equation will be won by four Art Square plus 1.5 plus two is expressed. It is two minus t on this will have two solutions or can be sold into parts complimentary in particular solution. Right. So come to Metis solution can be obtained by replacing the right inside or the external forces zero. So this is called take equation on solving this called equation. We get address minus two and minus Hold. Therefore I see will be see one here is two minus tooting. I see two days to minus 40 now 40 years were given that wiping must be of this form. So a plus B, it is two minus t. So why dash off key letting me Maybe it is two minus three times minus one and write about us. Whatever that's off, he will be be. It is to minus 30 and minus one square I two times it will come. So now this wipe solution off this defense allocation, the African satisfied the situation. So we'll have won by four. You know, be times it is two minus t like this is one plus 1.5 white house, which is B. It is two minus three times minus plus Y p, which is two times a plus B minus t to the question six President in dynasty. Okay, so now we'll separate the terms. It it is two minus T and time without it. So we'll have it is to minus t comments from here by four from here, minus 1.5 b. From here we have plus to be right, and the content is to a to A is it cost to six plus arrested dynasty. So I'm comparing. We get to weigh the cost to six therefore a three. And here, this time entire Tommy's being by four minus 151.5 plus two B equals to one. So I'm solving this. We get busy equals two. All right, three. So our solution is off. Whitey is three plus for three days to minus t. So a total solution. That is why I called y c plus wipe. That is equals to see one. It is two minus two. T proceed to it is to minus 40 plus three plus for three to minus t. Now the boundary Conditional Additional condition here in is why off zero is equals to now. Since it was a poor, it will be minus two. Right? And why they're so the U. S. Three so we can differentiate this and then we'll substitute two functions to initial conditions. So see one here is to minus 30 minus two. See to it is to minus 40 minus 40 for three days to minus three minus one. So first one will be substituted. Area second. Yeah, Okay. So why owes us minus two? Minus too easy for us to see when he is 20 See to it is 20 de here. Four by three. It is 20 Okay, so we have minus two is C one plus two plus three. So we get C one plus c to it. Because two minus five. Sorry, P plus four by three. So we get pieces minus 1993. Okay. Now for a second part. So why does off? Zero is 33 easy person minus two Syrian. It is 20 here, minus 42. It is 20 here, minus four brightly. He needs to zero. So we get calculation as crazy. Cause minus 27 minus 40 to minus four by three. And this gives us to see one plus four C two is equals to minus 33. So on solving this equation and this equation, we get value off. Stephen is equals to minus 21 Layton and C two e z equals to 25 six. Okay, so therefore, a final solution. Why? Off key is minus 21 by two to minus duty, plus 25 by six. Here is to minus 40 plus three plus four by three. Here is two minus D. I decide to find the value of two. Right. So Therefore, why off to will be minus 21 by two years to minus four last 25 or six years to minus four into two. Kate plus three plus four by three. It is two minus two. So I'm calculating this value we get. It s 2.989 which is approximately 2.9. Okay, and since it's positive is below the Canadian right and that isn't solution, thank you.

So using that your previous question of using, uh, a porter times X double crime plus 1.5 x prime plus two X equals zero using the initial point exterior. Clint. Um mais tu and ex prime of zero. You calling three way saw this. So you get X except T exit calling. C e minus two t put T minus 40 and my answering here clearly. C one C two Mine too. Ex prime of zero coin. Mind to see one place or think you is equal to my equal. Three. So see to Teoh he wanted people to minus five out of two X todo equals five to you May mean is, uh to t plus here, minus 45 I teel exit here he is about to he minus four plus minus eight to which is approximately six to so that's supposed to be 00 for six or by six to above equilibrium

Way. Read it to you. Live prime plus two. Why six plus heat? You make it this along with wife theory. Quinlan's Teoh. Why prime here with you for three? Why don't you find your three favorite too? Plus two wise hero that my forces are You are close to using those here. Why? Age seems to be one in my foot. Plus to be raised to t like you being here. It was the most of the teeth Wife prime minus B intermediate Teoh Why doesn't work be here? My team You insert into the above equation below and you'll get three quarters times like tea plus to a six plus e Be easy full too. And okay. My came to be whole See you one year was you He raised waste. Why is he received one? See to 19 which is equal Teoh. I mean, making divine religions equals last year C one plus C to Afghanistan. Why is equal to minus one? You my 42 c to the T. They're instant e of my key. My time on the errors be cold. Four c one to C 24 years just to three. So they're using these. It'll be forced. You won t to equal to thank you now very bright bakery. And the other one would be You want my Why three See while quote Teoh 25 divided Teoh too twi tete between my places Last week, one of my right to you 34 3rd


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