Compute the Laplace transform of the following functions. 1. y(t) = cos t·H(t - 27) 2. y(t)=te3 H(t-1) %3D 4. y(t) = sin t-H(t - t/2) 3. y(t)=eH(t-2) + 6H(t-3) 5. y()=(³ +1)H(t-1) 6. g(t) = t H(t - 2)

Q: 2b. Determine the solution of the following problem using the concept of derivative and integral…

A: The given problem is to find the Laplace transform of the given integral term function.

Q: Find the inverse laplace transform of the problem L-[- u+1 (u+1)²+1! L[f(u}] = F(t)

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Q: ÓSTAIN THE LAPLACE TRANSFORM OF THE FF: O ft) = -to COS 2t - t + t Csin 2t - cos at) © gt) 2 オ…

A: Laplace transform

Q: Determine the initial value of c(t) where the Laplace transform of C(s) is given by: (4s +1) s(s +…

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Q: 1. Determine the Laplace transform of the function: f(t) = e¬t sinh 2t + e¯2t cos t s - 2 2 | A.…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the Laplace transform of f (t) = e2t(3 sin 4t – 4 cos 4t) 3-4s 3-4s A. s2-4s+20 C. s2-4s+16…

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Q: Obtain the Laplace transform of the following function: S(1) = {2-t- sin(3t), t <0 0, 2-t sin(3t), t…

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Q: Determine the Laplace transform: 1. f(t) = -7(e^3t)[sinh(2t)] 2. f(t) = 5(e^4t)[cos(10t)]

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Q: Find the Laplace transform of f(t) = cos(2t) + 7 sin(2t). s+1 s2+4 _s+14 g2+14 s-14 s2+4 s+14 s2+4

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Q: With all initial conditions equal to zero, what is the Laplace transform of y(t) in -2) + 2y (t) =…

A: So:- y'' +2y' +2y=HtTake Laplace transform of both sides of the equationLy'' +2y'…

Q: Find the Laplace transform of 1. f(t) = [1u₂n(t)](2 sint - sin 2t) 2

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Q: Determine the Laplace transform of e-5t sinh(6t) · е s+5 s2 – 10s–11 6. s2 – 10s-11 s+5 10

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Q: 1. From the definition of the Laplace transform, compute L(f(t) for (a) f(t) = 4t (b) f(t) = e2t (c)…

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Q: 4 The Laplace transform of f (t) = {*. 0st<2 is: t2 2

A: We have to use Laplace transform integration.

Q: Find the Laplace Transform of h(t) =t² sin(2t) 4s2 –3 A H (s) (s²– 4) 3 3s2 – 4 (B) H (s) = (s²+4) 2…

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Q: 2 Determine the Laplace transform of f(t)-te"sin(3t) s-4 a. (s²-3s+5)² 6s-12 b. (s²-2s-6)² s-4 C.…

A: Given function is f(t) = te2tsin(3t)

Q: Determine the Laplace transform of f(t) = e4t u(t – 2) e-2s s-4 -2s s-4 e2s s-4 e2s s+4

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Q: Determine the Laplace transform of f(t) = e-3t sinh (2t) 2 s2 + 6s +5 s2 – 6s+5 s² + 6s+5 s2 – 6s +…

A: Use the following formulas to perform the Laplace transformation.  Leatft=Fs-aLsinhat=as2-a2

Q: Find the Laplace transform of f (t) = t2 cos t 53-s А. (s2+1)4 253-4s С. (s2 +1)4 2s3-6s B. 2s3 +4s…

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Q: * Find the Laplace transform -5 -21 sint f(t) = te' -21 s + 2 2s + 4 (s² + 4s + 5)- (s² + 4s + 5)? 0…

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Q: Find the Laplace Transform of h(t) = t? sin(2t) 12s?– 16 A H(s) (s²+4) 3 48² – 3 B H(s) (s² – 4) 3…

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Q: Find the Laplace Transform of f(t)= e"(2cosh 2t + sinh t). %3D 2s+3 A) f(s) = %3D s2-4s-5 2s-3 f(s)…

A: Le2t2cosh2t+sinhtApply transform rule:  if Lft=Fs then  Leatft=Fs-a.For e2t2cosh2t+sinht:…

Q: B: The Laplace transform of the; f(t) = e-t.sinh 3t

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: Determine the Laplace transform of the equation f (x) = 2e-"sin4t 16 A s2+ 4s + 20 20 B s2+ 4s + 20…

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Q: Find the Laplace Transform of h(t) = t? sin(2t) = ='s 3s2-4 A H(s) = (s2+4) 2 482 – 3 B H(s) =…

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Q: What is the Laplace transform of f (t) = e2" (sin 2t – 1)? 16s 16 s6s2 +16s12 6s 16 s 6s2+16s 16 16s…

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Q: x(t) = (t² + 4)e2t – e-t cos t

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Q: Find the laplace transform of t sin (t) A. 2s/(s2+1)2 B. 1/s2(s2+1) C. 1/s2 + 1/s2+1 D. -…

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Q: O xt) tLosh at - sinh 34 + ws (ot - )

A: Properties of the Laplace transform  Laf(t)+bg(t)=aL[f(t)]+bL[g(t)] Ltf(t)=-F(s), where…

Q: f(t)=e'(4 e2" + 5)?.

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Q: Find the Laplace transform of h (t) = 1.5 sin (3t – ;)

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Q: Give the Laplace transform of 5 0Sx and x <I f(x) = -7 sin (2x) 2 +e 2 4 +4 b) O Fe)-+" ( 5 F(s) 7 5…

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Q: Find the Laplace transform of - a. f(t) = [1 − u₂π(t)](2 sin t — sin 2t) t², -8 + 3t, b. g(t) = -…

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Q: Find the Laplace Transform of e-t sin2t 2 2s 2 A. ²/+ B. S (s+1)²+4 (S-1)²+4 C. S+1 s(S²+4) D. None…

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Q: ind the Laplace transform of f(t) defined by a. f(t) = 2 cos(120t + 45) ... b. f(t) = e-04t cos12t…

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Q: Find the Laplace transform of: 1. f(t) = e(-4t)[sin(2t) – cos(2t)]² 2. f(t) = V1+ sin t + (6t)13 +…

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Q: 1- Find the Laplace transform of the following functions Of(t) = (* – 3)² (b) f(t) = sin*4t (c)f(t)…

A: Since you have asked multiple questions we will solve the first question for you if you want any…

Q: Q1/ Find the Laplace transform of 1- f (t) = t² e cos 3t -2 x

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Q: FIND THE LAPLACE TRANSFORM OF y(t) IF ALL THE INITIAL CONDITIONS ARE 'ZERO’. d²y(t) dy(t) dt2 + 6 +…

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Q: Find the Laplace Transform of f(t) = t ei sin3t 6s A F(s) ((s- 2)²+9)? 6(s+2) B F(s) = ((s+2)²-9)?…

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Q: 1. Compute the Laplace transform of f(t)= u(t-3)e-²¹ (a) Using a table (ie using one of our…

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Q: 13. Compute the Laplace Transform of f(t) = t°e" +e* sin3t. 4 1 A) (s+ 2)'s² +4s + 13 2 B) (s –…

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Q: Calculate the Laplace transform of f(t) = 2 cos(3t)

A: The given function is ft=2 cos3t.

Q: 2. Find the laplace of the f(t) = t2 by using the laplace transform equation

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Q: Q3/ Find the Laplace transform of y(t)=e't Sin(t)Cos(t). a) 4(s-1)[(s-1)2+4]2 b) 2(s+1)[(s+1)2+4]2…

A: Given: y(t)=ettsintcos(t) To find: Laplace transform of given function.

Q: Find the Laplace transform of the function: 0, f(t) = { e - 10t + 26, t2 5 t < 5 1 L(8) = e-5s 52 2…

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Q: (b) Using Laplace transform, evaluate te -2t Cos 2t dt 0.

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Q: 2. Use Laplace transform to solve | cos(4t), 0T y" + 16y = ; y(0) = 0, y'(0) = 1.

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Q: Find the Laplace Transform ofe 2 cos3t + 5e21 sin3t s+2 15 A g2+9 s2+9 (s+ 2) + 15 в (s2+4s) + 13 15…

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Q: Take the Laplace Transform of both sides of the IVP y'' + y = 2δ(t-1) w/ y(0) = 1, y'(0) = 1 and…

A: Step:-1 Note:- Some Laplace Transform 1. Lδt-a = e-as   for a&gt;0 2. Lyt=ys  and  L-1ys=yt 3.…