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A car of mass 1300kg is constructed using a frame supported by four springs and a dash-pot with a damping 5% of critical. Each spring has a force constant 20 OOONIm...

Question

A car of mass 1300kg is constructed using a frame supported by four springs and a dash-pot with a damping 5% of critical. Each spring has a force constant 20 OOONIm: If the combined mass of four people in car is 350kg, determine the period of execution of two complete vibrations in seconds_ And then calculate the vertical acceleration experienced by the occupants at t=0.5s, given the initial displacement and velocity are 0 mm and mls respectively.

A car of mass 1300kg is constructed using a frame supported by four springs and a dash-pot with a damping 5% of critical. Each spring has a force constant 20 OOONIm: If the combined mass of four people in car is 350kg, determine the period of execution of two complete vibrations in seconds_ And then calculate the vertical acceleration experienced by the occupants at t=0.5s, given the initial displacement and velocity are 0 mm and mls respectively.



Answers

Four passengers with combined mass $250 \mathrm{~kg}$ compress the springs of a car with worn-out shock absorbers by $4.00 \mathrm{~cm}$ when they get in. Model the car and passengers as a single object on a single ideal spring. If the loaded car has a period of vibration of $1.92 \mathrm{~s}$, what is the period of vibration of the empty car?

So we know that the period secret to two pi over omega, which is two point times mass over cake. Right? So when they are, the car is loaded going to be equal to two pi the mass of the car, plus the mass of the four passengers, which is 250 overtake. Okay, so and we know that Hey, it's good to the force divided by the distance the Forces mg, which is the mass of the four passengers. Times 9.8 this is G Karsten. Give up by the distance, 0.4 metre is given by 6.125 times 10 to the four. He was him for meters. Put the okay back in here. We can calculate the mass. A sequel to E l or Okay, yeah. Over two pi career times K minus 200 which is 5.469 times 10 to the three Children. So when the car is empty, it just simply massive Jupiter mass of the car over. Okay, plug in the numbers. Yeah. The period is equal to 1.88 2nd

Eso for this question. It was asking us what is the period of vibration off the empty car? Well, we know the period is equal to one over frequency. We just went over and the for consider, right? You have to buy and give us two powerful omega, which is the angular frequency. And Omega is equal to the square root K o m. Which is the force Constant doing biomass. And we caught him back to the T question Will get through pi over square. Okay, over m, which will give us t 0 to 2 pi times. It's where, um okay, okay. And we know the force Constant K is equal to force to Dubai by the displacement. Okay, so Well, let's figure out, OK. First name for his case. It's okay to go. The force and force that is involving is the question. Is the gravity off the four passenger somebody? So is mg Okay? You have my axe. Remember that massive A four passenger was 250 kilograms. The gravitational constant is 9.8 year for seconds where any compressed four centimeter, according to the question So which is 0.4 meter and this will give us 61 250. I knew Tom a meter. Okay, so the force constant is Ah, 61,000 and 250. Your car per meter. So now we know that initial period was given as one point. Oh, a seconds. An initial period is equal to to buy Times Square root the massive passenger plus the mass of a car. Okay, over the force. Constant and ah, time here for the empty car is equal to pi. It has screw off the massive car over force. Constant. Huh? So now we have the forest constant. So in order to determine the time period for an empty car, we need to find out the mass off the car. Okay? And in order to figure out the massive a carpet and go back to the equation T i with two pi times square MP bus, EMC over K, because miss off the passenger skill, it was just 252. Okay? And we also know the force constant is 61,000. I'm sorry. 6000. 61,000 and one, 250. You know something meter and we know the time period for the car and a passenger. It is one point away sector. So this will give us MD car is just equal to t I. Which is the initial period over troop I square times, the force constant. And then my sister mass over the passenger. Okay, so this is from the this equation here. So this is to this, Okay? It was on simplification, and you'll get a question. I got down here. Good. So if we plug in a value, we'll get G I, which is 1.0, a second over to buy square times the force constant, which is just do you 1000 and 250. No tongue. Come here and minus the massive passenger was just 250 kill worms. And this will give us the mass of Emily Carr of. And the car is 2000 and 559 or in six two groups. Okay, No, for the period off the empty car is with the to buy times square room M car over the force constant. This will give us the periods just simply with the two pi Times Square. Oh, mescal. Car wishes 15 59. 26 kilograms over the force Constant, which is 61,000 and 250. Utah meter. Okay, this will give us the time. Here is about one point zero 0 to 6 seconds if we round up. So the third digits give us 1.3 second. Okay. And that's the answer. Forties question. Thank you.

They have driven here is that four passenger with combined marks off 2. 50 kg compress the stream off a car. Good one out. Stock absorb Bye. Four centimeters When they get in model that car and places are as a single body on a single ideally spring. A loaded car having that time Put it off 1.8 seconds Loaded card, then Can't put it off. Unloaded car were profile Another thing It as we know tampering off loaded spring is defined as thieves Culture to five. Rudolph Um Avanti. Suppose m is the mass of the card That time period in case off empty, it will be two points I am upon Kate here M is months of the cut Empty its passenger that is loaded who fight not total mass becomes mask off. Carless master passenger on Mars a passenger is given to 50 No value off you can find And these cultural cares Okay, baby And you waited masses to 50 9.8 on compression in the spring It four centimeters. That is fine. You're a poor meter. Okay, six point 1 to 5 and took 10 to the power foot nutrient permitted no dividing the question toe Enver. We can simplify solving decreases. Violent toe. We can write most of the empty car will be time with off loaded car square. But to fight K minus 50 it will be birth, while 08 it's quick upon to fight 6.125 10 to the power. Both. So most of the car. You will get a small emptory. Let me correct it. It will be 1.56 and 10 to the power three. Katie, so I can put it up. Empty car will be two fights. 1.56 10 to the power three upon Kate 6.125 10 to the power. Four seconds on solving it you will get temporary duty one ticket, the actual for it. Thanks for watching it.

In this question, we need to analyze the problem. The compression in the spring one is 50 cm. That is 0.5 m. And the spring to uh at the final position. The compression is uh 50 centimeters minus 30 centimeters. That is 0.2 natives. So first we need to calculate the force in the graph. So the fourth f. One when the spring one is compressed uh to 30 cm. So the fourth are fun equals The spring constant. That is 1600 Megaton Bomb Eater Into 0.3 m are afghan equals Uh 480. Notice. Similarly, the force exerted by the both of the spring At the compression of 50 cm equals the force exerted by the spring too. And that is uh 34 100 no. 10 m. And two 0.2 meters plus uh 1600 newton meter into 0.5 m. So the force f. two equals 1480 nutrients. Okay. Uh huh. Working by the force equals From the graph the area of the graph. And for the first person in the area of the triangle up to 30 cm. That is half into The force. That is 480 newtons into the base. That is zero three m plus the area of the tradition. And that is half into the some of the barrel. Said that is 480 newtons plus 1400 80 mutants Into the place. And that is 0.2 notice. So the work done by the four sequence Uh 268 tooths. And this work turned from the work energy tour. Um So from will energy to the world turned by the force equals the change in Canada technology. That is shelter. Okay. Since the initial cannot technology zero and therefore it is equals the final grand technology. That is half mv squared. So VF equals two times the welcome. That is 268 jewels upon the mass that is six 1000 kg and a square. Uh, the final Spirit is 0.299 m or second. So the initial speed is, let me correct something. The final speed is zero. So the voting by this thing is the initial kinetic energy and the shell, uh, Spirit is, this is the initial speed. Initial speed is 0.299 meters.


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