5

The Laplace transform F(s) of the 4-periodic function defined by f() =1 if 0 < t < 2 and f(t) = 0 if 2 < t < 4 is given byOF6s) OF(s)...

Question

The Laplace transform F(s) of the 4-periodic function defined by f() =1 if 0 < t < 2 and f(t) = 0 if 2 < t < 4 is given byOF6s) OF(s)

The Laplace transform F(s) of the 4-periodic function defined by f() =1 if 0 < t < 2 and f(t) = 0 if 2 < t < 4 is given by OF6s) OF(s)



Answers

Determine the Laplace transform of the given function. $$f(t)=t^{2}, \quad 0 \leq t<2, \quad f(t+2)=f(t)$$

For this problem. Well, right, this nominator as something squared, plus some constant. So we're going to be completely square. And if we look at as plus one squared, this is s squared. Plus two s, this one. And if we want to get to this denominator wishing to add one on both sides So as plus one squared plus one, is it? Well, the s squared plus two s plus two. That's our denominator. So we're gonna write this as s minus two, all divided by s plus one squared, just one. And we also know that negative too. There's nothing other than s trust. One minus three since plus one and negative three at too negative too. And we can separate. This is in the two fractions, namely, as plus one over s plus one squared plus one minus three over as plus one squared, just one. And now we're gonna take the inverse plus transform on both sides. So the inverse applies transform our capital F is gonna give us just some smaller half of tea. What would be the inverse of boss Transform s plus one over s plus one squared plus one minus three. China's Anversa plots transform of one over s plus one squared. Just one. Now we can use the believe first shifting fear. Um, since we have an s plus one in both of these spots, you know that we can then write this as e too busy. Negative. Two years since a will be negative. One of the inverse loss transform of s over s squared plus one minus three times. You need to The negative team turns inverse of loss. Transform of one over s squared, plus one. And now we're gonna use the rules for the plush transform of the sign and co sign right this as eat negative t factoring out on eating the negative t China is the universal questions form of this, which is just the co sign of t. So one is one squared. So be it. Just one minus three times. Same deal. One is just one square. Somebody is just one three times sign of tea.

High River. Today we're going to sort problem. Number six, if off is given less. Do you mind? Has through the whole square Indo you're drafty Love that stone from off Dave Square is in fact er thereby. Yes, rest to in president, which is a photo. Well, thank you. Order they as Cuba the miners through the whole square into you. Softy, loveless term so bad Second, she couldn't get up. You got You know that part off? Minus to us. Intertoto there. But yes, Cube, that's the question.

Okay, so I got the periodic function, which is defined as being eat the T between zero and one and its periodic with period. Big T is equal to one. So what is the LaPlace transform while from theorem 10.3 point three, the plaice transformers 1/1, minus E to the minus. Ask times period multiplied by the integral from zero to the period of each of the minus esti times by the function. So this becomes a very simple into girl. Andi, integrating this. We get minus this between zero and one. So evaluated at one. This is eat zero. So it's just one my minus one over us, minus one. And then that's plus because it's minus minus. Plus one over asked, minus one times. Sorry. Okay. So, yeah, we're evaluating T is equal to one and t Z zero. Right? So this is gonna be that and then minus, But then that's gonna be a plus. One over Asked, minus one. And that's it. Okay, so this is the answer to our problem. Okay. If we wish, we can combine it into a single common denominator. Okay? That's it.

Hello and welcome the problem. 10 Chapter six Section 3 here were asked to final applause transformation of the given heavy said function. Have you said functions. And um to do this we have to remember the golden rule of each little past transformations and that's that you subsea of T um times F of t minus C is equal to E. To the minus C. S. Times little plus transformation of um F. Of T. All right that is. And of course the left side is a little pot transformation as well. So with this we can just substitute this F. F. T minus C. For one because that's essentially what all of these are being multiplied by. So doing that we're gonna be left with E. To the minus s. Well what's a little past transformation of one? What's one of us? Because the plus transformation T. To the end that we found in previous sections is in factorial Over us to the end plus one. So plugging this in The zero factorial is one over S. To the zero plus one is one. Yes. So I left with one of our S. And well so the whole posture information of you won each of the negative s over us. Likewise we can repeat this process for the others. We get to E. To the minus three S over us And -6 e. to the -4 s. Over us. We can of course combine them to be E. To the minus S. Plus two E. To the minus three S. Find a six e. to the -4 s over S. and that concludes the problem.


Similar Solved Questions

5 answers
AIQ CV (I-e"RC) for an RC circuit what is 2 seconds after the switch is the magnitude of the current closed in the series circuit that contains & 8V power source, 10-uf capacitor; and ISK-ohm resistor?What is the voltage across the capacitor after 2 seconds?
AIQ CV (I-e"RC) for an RC circuit what is 2 seconds after the switch is the magnitude of the current closed in the series circuit that contains & 8V power source, 10-uf capacitor; and ISK-ohm resistor? What is the voltage across the capacitor after 2 seconds?...
5 answers
Question 4 (5 points) Saved What Isthe PH of a solution prepared by mixing 100.00 mL of 0.050 M HCI with 100.00 mL of 0.100 M NaOH? Assume Ihat tha volumos are addilive.12.701.607,0012.401.30Quectlan
Question 4 (5 points) Saved What Isthe PH of a solution prepared by mixing 100.00 mL of 0.050 M HCI with 100.00 mL of 0.100 M NaOH? Assume Ihat tha volumos are addilive. 12.70 1.60 7,00 12.40 1.30 Quectlan...
5 answers
Point) Suppose wwhere4 = 2 + sin(5t) , and z = 2 + cos(3t) _dw Use the chain rule to findfunction of T,9, 2, and Do not rewrite T, Y; and in terms of t and do not rewrite 01dwNote: Your answer should be an expression in T, Y; 2, and t; e.g: "3x - 4yda Use part 1. t0 evaluate when t = 0.
point) Suppose w where 4 = 2 + sin(5t) , and z = 2 + cos(3t) _ dw Use the chain rule to find function of T,9, 2, and Do not rewrite T, Y; and in terms of t and do not rewrite 01 dw Note: Your answer should be an expression in T, Y; 2, and t; e.g: "3x - 4y da Use part 1. t0 evaluate when t = 0....
4 answers
At a certain temperature,K = 9.40 x 10-4 for the reactionFeSCN2-(aq) = Fe3+(aq) + SCN (aq)Calculate the concentrations ofFe3-, SCN , and FeSCN2+ in a solution that is initially 20 MFeSCN2- [FeSCN?-] =[Fe3t] =[SCN ] =Submit Answeroy Anolher Versionitein attempts remtaimino
At a certain temperature,K = 9.40 x 10-4 for the reaction FeSCN2-(aq) = Fe3+(aq) + SCN (aq) Calculate the concentrations ofFe3-, SCN , and FeSCN2+ in a solution that is initially 20 MFeSCN2- [FeSCN?-] = [Fe3t] = [SCN ] = Submit Answer oy Anolher Version itein attempts remtaimino...
5 answers
Whal are the major assumptions thst Aenu MILidenl04'EaS A[ pressure Oi 0.95ualm Occupies ume ot15 Wml, temperalure [0 I(mL whal tic neu pressure 'exnundedcunatunieas at 4 pressure 0f7j5 mm. Hg.occupies volume of [20 UmL. Ifthe pressure j5 reduced {o 0.80Qa1t &1 constant lemperalure, what is the new volume?Woum
Whal are the major assumptions thst Aenu MIL idenl 04' EaS A[ pressure Oi 0.95ualm Occupies ume ot15 Wml, temperalure [0 I(mL whal tic neu pressure ' exnunded cunatuni eas at 4 pressure 0f7j5 mm. Hg.occupies volume of [20 UmL. Ifthe pressure j5 reduced {o 0.80Qa1t &1 constant lemperalu...
5 answers
Question 11 Not yet answeredFind the induced current in the coil at an instant t = 4s, for given instant - the flux related to the coil is $= At-3 8t-2 -12t +16. Assume the resistance of the coil is 8 Q 3 Marks (b)How does rms velocity of the gas changes if (i) Pressure of the Gas is doubled (i) Temperature of the gas become 9 times. Explain briefly: MarksMarked out of 5.00F Flag question
Question 11 Not yet answered Find the induced current in the coil at an instant t = 4s, for given instant - the flux related to the coil is $= At-3 8t-2 -12t +16. Assume the resistance of the coil is 8 Q 3 Marks (b)How does rms velocity of the gas changes if (i) Pressure of the Gas is doubled (i) Te...
5 answers
What funtional groups are in this molecule?A) ester; ketone, Idehyde B) ester; aldehyde C) ether; ketone D) ether; aldehyde ketoeWhat are the respective shapes around the boron atom in BH: and NaBH:? A) trigonal planar and tetrahedral B) trigonal planar and trigonal pyramida C) trigonal pyramidal, and tetrahedral D) linear and trigonal planar
What funtional groups are in this molecule? A) ester; ketone, Idehyde B) ester; aldehyde C) ether; ketone D) ether; aldehyde ketoe What are the respective shapes around the boron atom in BH: and NaBH:? A) trigonal planar and tetrahedral B) trigonal planar and trigonal pyramida C) trigonal pyramidal,...
4 answers
6.Determine the standard deviation of the reduction in Blood pressure for subjects with no exercise program: 7.Determine the standard deviation of the reduction in Blood pressure for subjects on daily exercise program Determine the variance in the reduction in Blood pressure for subjects with no exercise program Chojces for 6 to & a) 8.56 b) 10.20 c) 11.41 d) 12.05 e) 12.55 D) 15.40 g) 24.90 h) 27.50 1) 73.26 j) 104.04
6.Determine the standard deviation of the reduction in Blood pressure for subjects with no exercise program: 7.Determine the standard deviation of the reduction in Blood pressure for subjects on daily exercise program Determine the variance in the reduction in Blood pressure for subjects with no exe...
5 answers
He alkyl halide shown can undergo an intramolecularFriedal–Crafts alkylation reaction. Identify the mechanistic steps,then draw the product.
he alkyl halide shown can undergo an intramolecular Friedal–Crafts alkylation reaction. Identify the mechanistic steps, then draw the product....
5 answers
Solvt M Sy,, km of kiacer egcetion} uSn$ Yn< (oajus Torj ar elim {0c1ic 72 m-92 9 0 * 414 (4
Solvt M Sy,, km of kiacer egcetion} uSn$ Yn< (oajus Torj ar elim {0c1ic 72 m-9 2 9 0 * 414 (4...
5 answers
Give 2 example of protein structure solved using NuclearMagnetic Rosonance method (NMR). You must describe how method wasused and structure
Give 2 example of protein structure solved using Nuclear Magnetic Rosonance method (NMR). You must describe how method was used and structure...
5 answers
Section C: totol Pick anx 2 from the following questlons 2 * (6+2) pts [ONLY do Z04! If you do ALL uil take thc lowest gradeslul C1: Hydroboration and oxymercuration of 1,2-dimethylcyclohexene each dead ftQ two slightly different products Identify these structures using working mechanism for each_ Include any and all stereo as requlred:Hg(OAc)z HzO NaBHaBH32 HzOzIOH-
Section C: totol Pick anx 2 from the following questlons 2 * (6+2) pts [ONLY do Z04! If you do ALL uil take thc lowest gradeslul C1: Hydroboration and oxymercuration of 1,2-dimethylcyclohexene each dead ftQ two slightly different products Identify these structures using working mechanism for each_ I...
5 answers
Charge A and Charge B are 3.86 apart, and charge A is +1.72 Cand charge B is +3.98 C. Charge C is located between them at acertain point and the force on charge C is zero. How far apart fromCharge A is charge C?
Charge A and Charge B are 3.86 apart, and charge A is +1.72 C and charge B is +3.98 C. Charge C is located between them at a certain point and the force on charge C is zero. How far apart from Charge A is charge C?...
5 answers
Question 2 Suppose R is a commutative ring with identity, ad P € R is a prime ideal Let S =R P. Show that J = {S:aeRbes} is the only maximal ideal in Rs: (A ring with only one maximal ideal is called a local ring )
Question 2 Suppose R is a commutative ring with identity, ad P € R is a prime ideal Let S =R P. Show that J = {S:aeRbes} is the only maximal ideal in Rs: (A ring with only one maximal ideal is called a local ring )...
4 answers
GPfe 2 283228888 8 28 8 6 8 6 1 V 82 8 2 8 5 13 J2e80 7 8 8 ?0 @ J6'88 8 [3888288 28228
GPfe 2 283228888 8 28 8 6 8 6 1 V 82 8 2 8 5 13 J2e80 7 8 8 ?0 @ J6'88 8 [3888288 28228...

-- 0.028021--