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You (mass mj 76.5 kg) stand on platform of mass mz 42 kg The platform executes simple harmonic motion in the horizontal direction with period of 2.6 When the platfo...

Question

You (mass mj 76.5 kg) stand on platform of mass mz 42 kg The platform executes simple harmonic motion in the horizontal direction with period of 2.6 When the platform is maximum displacement; you step off the platform gently: What was the total energy of the system before you stepped off the platform, If the maximum speed was 7.1 mIs?NumberUnitsWhat is the new amplitude of oscillation after you step off?NumberUnitsFind the maximum speed after YoU step off.NumberUnits

You (mass mj 76.5 kg) stand on platform of mass mz 42 kg The platform executes simple harmonic motion in the horizontal direction with period of 2.6 When the platform is maximum displacement; you step off the platform gently: What was the total energy of the system before you stepped off the platform, If the maximum speed was 7.1 mIs? Number Units What is the new amplitude of oscillation after you step off? Number Units Find the maximum speed after YoU step off. Number Units



Answers

(II) An object with mass 2.7 $\mathrm{kg}$ is executing simple harmonic motion, attached to a spring with spring constant $k=280 \mathrm{N} / \mathrm{m}$ . When the object is 0.020 $\mathrm{m}$ from its equilibrium position, it is moving with a speed of 0.55 $\mathrm{m} / \mathrm{s}$ . (a) Calculate the amplitude of the motion. (b) Calculate the maximum speed attained by the object.

So we need to calculate the speed and the maximum amplitude. So this is this system is undergoing simple harmonic motion and we can say that the mass is going to be equal to two point seven kilograms. We have a spring constant of three hundred ten at Newton's para Meter, and then we have a compression or rather, just a spring displacement of point zero two zero meters and a velocity as point five five meters per second. So we can say that energy total for parting energy total equals one half and the square to the potential energy plus one half K X squared, and this is going to be equal to one half k a squared. So this is instance, essentially at when the spring is compressed point zero two zero meters, the object the masses going point five five meters per second. And this is all going to equal of the maximum potential energy of a spring, which would be half times the spring constant times the maximum amplitude squared so we can say that the amplitude is going to be equal. There's going to be equal to the square root of M V squared, divided by K plus X Square and solving for this, we can say that I am so two point seven point five five squared. This will be divided by the spring constant of three hundred and ten and then plus point zero two two squared. And we have that the amplitude is going to be point zero five five meters now. Saying What's his maximum velocity after the spring is fully fully deep. Decompress essentially. So we can say that for part B, the energy total energy told that protect the total potential energy of the spring is going to be equal two one half and be squared. So this in this instance, all the maximum potential energy of the spring is all being converted to put into kinetic energy. And then at this point, we can just solve for the velocity and said There's going to be time. There's going to be equal to the amplitude of the square root of the spring constant divided by the mass. And we can say this can be equal to point zero five five times the square root of three hundred and ten, divided by the mass of two point seven and the velocity is going to be point five nine zero meters per second. So this will be our final answer. That is the end of the solution. Thank you for watching.

Mm hmm. In the first part of this problem, we are going to calculate the aptitude of those lighting system that is a in order to calculate those lessons. Also, amplitude of those lighting system We need to write the equation for the total energy as you as equals to one divided by two. Okay, square. From here, we can write the equation for this A as a as equals to To you divided by K square root. So this would be adequate. Number one, Let's put the values into the square. And so it will be air squared of two into 67.6 times old divide by K, which is equal to 63.7 Newtons per meter. So from here, we can write the value for this A s A is equal to 0.49 centimeter. Let's move toward the party of this problem. So, in part B, we are going to calculate the speed that is we We can write the equation for the we as well as equals two omega squared of s square, minus x square. So it, uh, X equals to zero. And this we will be the maximum and this can be written as we maximum is equals to Omega. Let's put the values into this question. So it will be we maximum Z equals two. Every day is equals two 0.49 Multiply it in response minus 2 m into omega, which is equals to 2.38 radiant per second. So from here, we can wire the value for this. We maximum as we maximum is equals two 1.17 Major prosecutor. So this is a required answer. So it was we make some, um, thank you.

As we all know that the period of mass attached to the spring is given by T is equal to two pi blue tender and by Kay, and the first constant K is equal to to buy Uh huh, Holy Square Multiplication m So simplifying it further than putting the value I can write the expression edge to buy multiplication 2.6 Holy square Multiplication 1.8 On solving I get 479.88 Newtons per meter. Now, as we all know, that the energy is equal to one by two k squared. So simplifying it, I can write one by two Multiplication 479.88 Newtons per meter multiplication 0.71 m squared, which is equal to 1.21 jewel as our answer.

In this problem. We all know that time period is equal to two pi route under em by K So the first constant K can be written it to buy f holy square multiplication m So just putting the value years So two pi multiplication 2.6 Holy square multiplication 1.8 and on solving a gate evaluate 479 0.88 Newton per meter Going forward as we all know that the value of energy is equal to half a k a square. This is the formula, so I can write. E is equal to one by two multiplication 479.88 Multiplication 0.0 71 is squared and on solving it. I get the value of e H 1.21 Jules, this is our end.


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