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The displacement of particle on vibrating string is given by the equation s(t) in centimeters and in seconds Find the velocity of the particle after secondssin(147t...

Question

The displacement of particle on vibrating string is given by the equation s(t) in centimeters and in seconds Find the velocity of the particle after secondssin(147t} where is measuredv(t)cm;s

The displacement of particle on vibrating string is given by the equation s(t) in centimeters and in seconds Find the velocity of the particle after seconds sin(147t} where is measured v(t) cm;s



Answers

The displacement of a particle on a vibrating string is given by the equation

$s(t)=10+\frac{1}{4} \sin (10 \pi t)$

where $s$ is measured in centimeters and $t$ in seconds. Find the velocity and acceleration of the particle after $t$ seconds.

All right, since we are given S of T uh is 10 plus a 1/4 signed of 10 pi t. The theme in this problem is when they ask for velocity, that's the same thing as the derivative of that. Uh and just a reminder that the derivative of a constant is zero. I'll go and write that for right now. And then what we have going on here is the chain rule where the first thing that you do is you take the derivative of the outer function. So the derivative of sine would be the outer function is co sign. And what you do first is and leave the inner function alone. But I have to multiply by the derivative of the inner function. And because T is your independent variable, It's just a constant times t. So the derivative of that would be 10 pie. So when you go to clean up your answer, You know, 10/4 reduces to 5/2. You can stick that pie in the new numerator. Tell you multiply fractions Of 10 PT. Co sign of temp it and that's your answer for velocity and we're done at a unit to it are good.

The way they wish it can be read in the US a sign to buy over them. Duh x minus to buy f D. The amplitude is given by 0.45 The report 45 Mater over Do sign to buy over website is given by 1.8 meter X My ass Dubai frequency is given by 12 lives past every minute, so 12 wave passes every two minutes. So 120 seconds dynasty. So that comes out to be syrup or and to do five meter sign to buy over 1.8 meter x minus by your six second t.

No. In this given been given the immigration off deposition as this on, we have to find out the instantaneous velocity on that survey nation. Be equal to feel second and be equal 2.3 seconds. Do that. First we find our attention. Penis velocity, new genetic don's, which we find out by differentiating are with respect to be reduces 30 years to minus straightly. I plus 60 a few days do Hi. Nice to be okay. Course 15 d minus date is to be signed being you and citizen millimeter seconds. Now it's very lonely. We find out instantaneous acceleration by different shooting velocity the last time Now, So acceleration will be my last 90 He raised to illustrating I bless. Fact it, dude. Minus 1 20 he raised to a minor Studi class. If pinky minus 900 years to minus duty, sign 15 deep minus 1 20 You toe minus to B close off the empty plus 16. Unity is to remind us to be sign 15. Now, after thing we find this he get minus 90 years minus three p I. And this is she, Unless minus do 40 us to a minus two p close off 15. 90 minus 884 Be raised through my last two p Sino 15 p. She now this is in millimeter per second squared. So now that important, uh, gentle form off velocity and acceleration We want to substitute the values to find at many people he becomes tarty. I bless 60 j 1,000,000 litre, four seconds Onda acceleration becomes why most 90 I fine us to 40 Really meter or second squared. Similarly, at these equal 2.5 seconds, we have velocity as qwerty He minus 1.5 I yes, 60 e is to minus one gloss off 7.5 minus eight years to minus one Sign off 7.5 Now, after putting this just letting this in a calculator, we have 6.6 long for I left for point a nine one Jane meter meter for a second. So acceleration also becomes just updating your bonfire in Durban. Appreciate. 90 years to minus 1.5 I plus minus two far be, do you say? Still minus one course or 1.5 minus 884 year raise to minus one. Fine. So in 0.5 now, before doing this too. Do this day. The following is too. We have minus 20.0 A I minus 335.65 Let me but second squared. And us You have the answer.

Hello students in this question A string vibrates according to the equation Y equals 25 signed by extra whereby three cause 45 3. Okay, so for the part A we have to determine the speed of the component waves. We so we can write that we it is equal to omega divided by K. And omega. From here it is this value Okay, 45 K. Which is equal to this value by by three. Okay, so from here we get a speed. We it is equal to 1 20 and X and Y both are in the centimeters so this value will be in the centimeter per second. So this becomes the answer for the part A Okay. Now for the part B we have to determine the distance between adjacent nodes. So the distance delta X between artisan notes. It is equal to lambda by two. Always and this by by three is the value for the K. And we know that K. It is equal to two by by lambda and it is equal to five by three. So from here we get lambda, it is equal to six centimeter because this case is in the centimeters so delta X will be equal to six centimeter divided by two. So delta X is obtained as three centimeters. So this becomes the answer for the part B of the problem. Okay, now next we have to calculate for the part, see what is the velocity of the particle on the string at reposition X equals to 1.5 centimeter and T equals to nine by eight seconds. So differentiating the situation. So we will get that speed of the particle V. P. This is equals to deal by bad deal T. So differentiating the given a question with respect to T. We will get that five signs by X x three. This will be constant. Okay and differentiation of course cheetah is minus. Scientists are so minus sign 45 T. And differentiation of this. 45 B will be equal to 45. Okay Now we can substitute these conditions so we will obtain that VP it is equal to five signed by by three Marbler by 1.5 centimeter. So 1.5. This can be written as three by two centimeter. Okay and minus sign 45. More popular by this T. Which is equal to this nine x 8. Okay and multiplied by 45. Okay so from here we can see that this value will be obtained as by by two. So signed by by two is equal to one. Okay now solving the situation so it will be equals 25 and this is equal to sign 45 5 and this is the multiple of pi. So hence sign 45 pi become equal to zero. Okay, so hence this complete value become equal to zero. Okay, So hence we get from here, the velocity of the particle on the string is equal to zero. So this becomes the answer for the party. Thank you.


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