a-block-attached-to-an-ideal-spring-undergoes-simple-harmonic-motion-the-acceleration-of-the-block-h

Question

A block attached to an ideal spring undergoes simple harmonic motion. The acceleration of the block has its maximum magnitude at the point where
(A) the speed is the maximum
(B) the speed is the minimum
(C) the restoring force is the minimum
(D) the kinetic energy is the maximum

Sachin Rao · Accepted Answer

the problem. We have given a block attached to an ideal spring, and it goes a simple harmonic motion. The exploration of the block has its maximum magnitude. So we know that acceleration is equal to minus omega square X. In simple harmonic motion, we had access the displacement. When access maximum, it is equal to amplitude. So the maximum value of exhalation is equal to omega is square a right. That means suppose this is a mean point. And this is that. And this is negatively. That means at this point, exhalation is maximum. Right? So we&#x27;ll go out. Uh huh. All right. His speed is maximum. Speed is maximum. Yeah. Speed comics. Some of the main point. So you look at it. It&#x27;s pretty as many of the speed as many. Right? That also there is tweeting forces. Many MKX. Yeah. Zero of that. Got to Lorraine. Mhm. Mm. Mhm. Google. It kind of energy is mixing up. Mhm. Yeah. Mhm. Okay, well, mhm. Help me. Look. Here&#x27;s Andre. You

Jilin Wang · Answer

Okay, so for this question, I&#x27;m not going to tell you the exact the answer off. But I&#x27;ll teach you how to do it. And you can you circle the herd to find things so we know that without express the position Oh, the motion as X equal to the ampule Times co sign angular frequency times time asked the initial face five. Right. So the velocity is the derivative off position, So we have d x d t They have negative. Owe me a P MP you time sign on the dotted. Similarly, the exploration is DVD. So you have negative Omega Square. A close eye on me. Right? So for question A is asking for the force countered. Okay, so we know that a force equal to negative k x and you go, Jimmy right in this question, we know the mass. We know the acceleration, and we knew the position we can define. Okay, go to navigate m A over X. You can also, dear, if this equation from this re questions, So if we take Yushin One and the Christian three here, or use a divide by axe, you can get exactly the same results here only the only difference is that here you have kay and am But here, you&#x27;re gonna have Omega Square. So you Because we know that Omega is secret. You square it, children. Right? So was dizzy reissue by exactly the same answer. So once we find Kay, we can also use this. The mission to find the anger for the ceiling. This for questioning a question. Be mpv off the motion here. We can use energy conservation. All right, so we know that the total energy is secret to the Maxima Kinetic energy, which is half a a square. All right, So are we already know Kay from questioning. And is he good to you at any moment? The kinetic energy X squared? That&#x27;s a potential energy. Sorry. This is a petition urging the X square plus neck energy envies good. We know the mass. We know the velocity when Okay, when you acts, we can use this inquisition to find what stamping. So in this case and figure this secret you Sharon a scare. I X script us and over. Okay, please. Right. That&#x27;s him. Questions. See what&#x27;s the Okay. So, for questions, see, what is the maximum speed So if we look at the expression of the velocity here, so when sign would you want it will have its Maxwell speak, which is so the max on a vehicle too omega I&#x27;m standing. We already know the amplitude down here you can find similarly for D the maximum acceleration. It&#x27;s gonna be yes, only us clear times. Damn you. And you can plug in the number with your catheter and find financing.

Derek Walkama · Answer

Okay. VX equals plus minus the square root of K over M times the square root of a squared minus X squared. This is just for simple harmonic motion Rearranges for a equals The square root of M the X squared over K plus x squared. If we plug everything we know, we know the mass. We know the ax swing. Okay, you know, X, we get 0.38 meters. We also know that X equals negative Omega Squared X, which equals negative K over M X. Again we plug in everything we know. Um, sorry. One more step here. Maximum acceleration happens when X is the largest. Will that occurs when X Is that a So we can replace us with a exes. Largest when it&#x27;s at full amplitude. And then we get 59.26 meters per second squared. Finally, the force equals negative K x, its maximum at at negative A. So this is negative K times negative, eh? Which equals K A, which equals 1 19.7 Newtons.

Deepak Kohli · Answer

Hello, Strains. Let&#x27;s start our discussion. Suppose Ah, block off. Unknown mask is attached to a spring and the spring constant is 6.5 New temple meter. The amplitude off this motion is 0.1 meter. Understand? Sentimental in meter it is or 10 inmate. Raise it 100.1 meter. Okay, No at the display at the position when it is just half way between equilibrium position on the extreme position. That is an important support. This is the equilibrium position the position there No forces directing at extreme position When it is accent extended with the fourth, the amplitude is maximum at one. The displacement is a question amplitude So when the position is just half way between a Taliban position and the endpoint, then speed is 30 centimeters per second. Speed off motion. So in media it is when? Three meter per second. Ok, eso displacement is half way. It means that it is the half off the amplitude. Okay. And 0.1 by two. And that is Jiro. When Joe fight meter. Okay. No, you have to find out that miles off the block. Okay. See, we have the formula off velocity Omega under route a square minus X squared. Where is the amplitude? Access the position. Or may guys, the angular frequency envies de velocity After squaring what side? We will get Omega Square. It&#x27;s quite minus X squared. Value for Mega Square is four Coast force constant by em. We have to find out the value off and so it will be. See s square minus X squared by the square. No, By putting all the values that is 6.5, my bracket 0.1 square minus or NGO five square upon 0.3 meters per second. Squared his velocity. Oh, it is 13 meter per second. Ok, uh we will get the value off masses. Jiro, 0.16 to 5. Cagey. No, we have to find other time. Beat it. Okay, so basically, you will be Dubai under your displacement by acceleration. Okay. Oh, we have to use an under formula and anglers frequencies that question too. Bye. Bye time, Peter. So time period will be to buy by Omega. Value for Omega is that would see by him. So it will comes like that. No putting the values two into 3.14 in tow under road Jiro 0.16 to 5 upon fourth course thing that IHS 6.5 new temper meter. So we will get the value off Jiro 0.99 2nd That is approximately equals toe one second. Okay. This is the time, Peter. No, We have to find out the maximum acceleration. So it will be It will make a square value of forming a square. Cib I am so by putting all the values that is 0.1 into six point five upon 0.16 to 5 kg, we will get get the value off exploration. Max will be for four. Meet up for a second square. Okay, well, this is all for me for this video. I hope you will like the video. Thank you.

Ryan Hood · Answer

in part A. We want to figure out what the acceleration of the motion it&#x27;s to do this, we&#x27;re going to use energy conservation in the extraction. And so we have the connect energy 1/2 l V squared, plus the potential which is 1/2 k. Explain. This is Eagle to the total energy which we know to be of form 1/2 k. Hey, scored now at tea is equal to zero. We know that X is equal to zero and we know that V is equal to negative 12 meters per second. And so if we analyze this equation, which is true for all values of X but we just analyzed X is equal to zero. This term here goes away and then we can solve for the amplitude in terms of the velocity which we know. And so we get that the amplitude is equal to the negative velocity Time&#x27;s a squared of mass over spring constant and so we can plug in 12 here and then the values here given to the problem and so is 0.956 meters. And that&#x27;s an answer to a in part B. We want to hear what the maximum acceleration is. And so Newton&#x27;s second law implies that acceleration is negative force, which is minus cakes over the men&#x27;s. We know that the maximum acceleration of a harmonic oscillator occurs at the end points where X is equal to the amplitude. So the max acceleration is equal to X when it&#x27;s at the ample to here. And then I just took the absolute value. So I removed the negative side, lucky and values. Here I get a value of 151 meters per second. Weird is the maximum acceleration, and Parsi recall that the force is equal to minus K X, and so the maximum force is equal to minus K Time&#x27;s the Maxwell Max, which is a I&#x27;m just going to take the absolute value this for the same reasons as above here. And so this implies that the maximum force is equal to 301 news. Whenever you plug in the cave that the problem gives us and the A that we found in party. This&#x27;s the newts, and that&#x27;s a silencer

Keshav Singh · Answer

Yeah, for this problem. On the topic of periodic motion, we&#x27;re told that a small block is attached to an ideal spring and is moving with simple harmonic motion on a horizontal fictional surface. Were given the amplitude of the motion as well as the blocks maximum speed and asked to calculate the maximum magnitude off the acceleration off the blocks. So we know the mechanical energy in the system is conserved and the maximum acceleration occurs at the maximum displacement. Since the motion is simple harmonic so by the conservation off energy, we know that the maximum kinetic energy ah, half m the Max square where we, Max the maximum velocity of the block must be able to the maximum potential energy. So that&#x27;s a half came a square. So this is elastic potential energy where a is the amplitude of emotion and we also know that the maximum acceleration for simple harmonic motion a Mex is equal to que a over m where m is the mass of the block and K is the force constant off the spring? Now, if we rearrange the initial equation from the conservation of energy, we get that que over em is equal to V Max over the amplitude all squared. And since we have these values, we can calculate k over em. So this is three 0.9 meters per second over the amplitude which is given as 0.12 m and all off the squared gives us a value. Okay, with them to be 1000 and 56 on this is in per square second. So now we can use this and calculate acceleration from our expression AMX. The maximum explanation has magnitude k times a over m So this is the value k of m times the amplitude which is 1000 and 56 per square. Second, I&#x27;m the amplitude 0.12 meters and hence we get the magnitude of the maximum acceleration off the block to be 127 m per square second

Problem

A block attached to an ideal spring undergoes sim…

Problem 2 Easy Difficulty

A block attached to an ideal spring undergoes simple harmonic motion. The acceleration of the block has its maximum magnitude at the point where
(A) the speed is the maximum
(B) the speed is the minimum
(C) the restoring force is the minimum
(D) the kinetic energy is the maximum

Answer

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