Find the Laplace transforms of the following functions: 3 -4 (s + 3)² + 16 4s2 – 4s + 2 (s – 1)3 13 3s (s – 3)2 + 4 f(t) -e-31 sin 4t + 3 Ans. f(t) = (t + 2)²e' Ans. f(t) = 2e3t sin 2t – 3e³ª cos 2t Ans. -

Q: 1- Find the Laplace transform for these functions (a)f(t) = e3t + 8 (b) f(t) = cos(6t) + 7sin(2t)…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Solve the following problem using Laplace transforms.  utt = c2uxx − g, x > 0, t > 0,  u(0,t)=0, t…

A: We have following problems: utt=c2uxx-g, x>0,t>0 Taking Laplace both sides…

Q: 2. Solve the following IVP by using the Laplace transforms. Choose ONE problem: (Hint: No need to…

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Q: 2s- 1 What is the value of the inverse Laplace transform given by g2 +2s +3 O a. et (2 cos(/2t) –…

A: Let's find.

Q: The Laplace transform of L[2 sin 6t sin 3t] is 2s s2 + (3)2 s2 + (9)² s + (3)² s2 + (9)² | s2 + (3)²…

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Q: 8 The inverse Laplace transform of the function is sin(3t) (A) t – 3 sinh(3t) (B) t- 3 sin(3t) (C)…

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Q: What is inverse Laplace transform for the following function? 3s + 2 s² + 2s + 10) a) =e=l cos 3t +…

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Q: * Find the inverse Laplace transform for-1 1 F(s) s – 2s + 5 1 -e²"sin2t 2 1,2'sin2t e'sin2t خيار 1…

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Q: 0. O hlt)= if t< 4 Find laplace transform for + cos(st) if +Z¢ 'a) e-4s e 40 s cos(20) + 5 sen(20)…

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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: 3.15 - Find the inverser Laplace transform of the following functions: 5e-2s d. G(s) = (s+1)(s²+s+1)…

A: Solution is given below:

Q: Find the Laplace transform of 6e'cos2t - e 6(8– 5) (8 - 5)2+4 8-7 6s В (8 – 5) 2+4 S- 7 s2+4 s-7 (s…

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Q: Find the Laplace Transform of cos(2t) + 7sin(2t) s – 14 A s2+2 14 B s2+4 $2 – 4 s+ 14 s²+4 14 D s2+4…

A: Given f(t) = cos(2t) + 7sin(2t)

Q: Determine the Laplace transform of (1 + e-t)2 7s2-7s-10 a. s(s+1)(s+2) 14s+2s+13 b. s(s+1)(s+2)…

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Q: Find the Laplace transform of t², -8 + 3t, 2. g(t) = - 6)² + 2 cos cos (1-2), 6 0 2

A: given g(t) is defined in (0,2)

Q: 3s+2 4. s² – 8s +25 5s2 +8s – 1 5. (s+3)(s²+1) |

A: Given Laplace Equation 4.) 3s+2(s2-8s+25) 5.) 5s2+8s-1(s+3)(s2+1) linearity property of inverse…

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: The Laplace transform of L2 sin 6t sin 3t] is S - s + (3)² s2 + (9)2 S 2s + (9)* s2 + (9)² s² + (3)²…

A: Solution by using trigonometric identities and Laplace transform table as follows :

Q: The Laplace transform of L[2 sin 5t sin 4t] is_ 2s s² + (1)² s2 + (9)². 2 s2 + (1)² s² + (9)² . s +…

A: L[2sin5tsin4t]We know,…

Q: Find the Laplace transform of 6e5 cos2t - e7t 6. 1 A s+4 S- 7 6(s - 5) 1 B (s – 5)2+4 s – 7 (s- 5)…

A: Given f(t) = 6e5tcos2t - e7t

Q: Determine the Laplace Transform of e1- c cos /7t + sin V5 4. sin /5 12s-7 s2+7 none of the choices 4…

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Q: Find the inverse Laplace transform for - 3t . ft) = %e* 7 (a)) F(s): %3D (s +3)3 , fGt) -e(2 cos 3t…

A: Inverse laplace transform

Q: Find the inverse Laplace transforms of 1 F(s): s2 - 8s + 15 1 F(s)= %3D s2 - 8s + 16 1 F(s): %3D s2…

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Q: 8 3 Find the Inverse Laplace Transform of- + 3s2+ 12 s2– 49 3 4 A) - sin2t + -cosh ( 7t) 7 3 4 –…

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Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s²-12s-87 1) L-1…

A: Given problem:- Find  L-1[(-3s2 -12s-8)/(s+2)3]

Q: 2. Determine the inverse Laplace transforms of the followings: (a) L-1 s2+2s – 3 4s - 3 (b) L-1 s2…

A: Laplace Transform: The Laplace transform is defined byℒf(t)(s)=∫0∞f(t)e-stdtwhere f(t) is defined…

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: -2sin4t Determine the Laplace transform of the equation f (x) = 2 e´ 10 A s²+4s+20 8 B s²+4s+ 20 20…

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Q: Solve for the Laplace transform of et sint cost cos 2t cos 4t 7+4s+20 82-4+20 -4+68 4s+8

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Q: What is the value of the inverse Laplace transform given by L 2s+1 8 J s2 +2s +3 O a. e-t (2…

A: Some Laplace inverse transform formulas: L-1(s-a)(s-a)2+b2=eatcosbtL-1b(s-a)2+b2=eatsinbt

Q: 3s-10 Find the inverse Laplace transform of F (s) = s2+4 O f (t) = 3 cos(21) – 5 sin(2t) O f (t) = 2…

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Q: 5. Determine the Laplace Transform of te2t cos5t s2-2s+11 a. (s²+4s–29)² s2+2s+21 b. (s2+4s+13)2…

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Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = £{f(t)} and n = 1, 2, 3, . . .,…

A: If f(t) is a function of t defined for all positive value of t, then the Laplace transform of the…

Q: Find the Laplace Transform of e 2 cos3t + 5e 2 sin3t - s+2 + s2+9 15 A. g²+9 (s+2) + 15 (s2+4s) + 13…

A: To find the laplace transform of given function first we will use the linearity property of laplace…

Q: Find the laplace transform of f(t) = e-3t cos nt s+3 82 -6z+9+7? 8-3 s +6x+9+n 8+3 s2 +6s+9+7 8-3 g2…

A: Solution

Q: (4) 3 2s-4 1 s2+4s+4 s+2 s2+4s+5 5s-6 s2 –3s

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Q: Find the Laplace transform of (e^ (2t)) sinh (4t) (-s^3 + 11s 2 1. (e^ (3t)) cos (5t). A. 56s + 196)…

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Q: E- Determine the Laplace Transform of cos 7t + sin v5· 4 sin 5 - 128-7 s2+7 4 sin 5 12s-7 82+7 V5 s2…

A: The solution is given as

Q: Determine the inverse Laplace transforms. (3s² + 8s + 9 (a) f(t) = L-1 (s + 2)3 s2 + 11s + 20 (b)…

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Q: 1- 3s Find the Inverse Laplace Transform of G (s) = s2+ 8s + 21 13 re A 8(1) = - 3e -'cosh(V51) +…

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Q: 4. Determine the Laplace transform of (1 +et)2 7s2-7s-10 a. s(s+1)(s+2) 14s2+2s+13 b. s(s+1)(s+2)…

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Q: Q3: Find the solution of the Laplace transforms of the following functions: L-1 ¹ [-35 -3s2-12s-87…

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Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s²-12s-87 L-1 1)…

A: Let's find inverse laplace 9f given function.

Q: * Find the Laplace transform for -4 f(t) = e'sin2t + e'cost S s + 1 + 2 s¯ + 1 s* + 2s + 5 s - 2s +…

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Q: Find the Laplace Transform of cos(2t) + 7sin(2t) S- 14 A s2+2 14 s2+4 s2–4 14 s2+4 s2+4 s+ 14 s2+4

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Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, . . .…

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Q: Determine the Inverse Laplace transform for 5s + 2 C-¹{² +65 +13) 1- f(t)= 5e³ sin 3t+ 13 e³ cos 3t…

A: Given problem:-

Q: (2) Find Inverse Laplace transform for; 3 1 (1)F(s) = 3 (2)F(s)= s2 +4 (3)F(s)= s (s +1) s (s² +16)…

A: Given:                 Question 4: F(s)=2s2(s+4)                 Question 5: F(s)=1s(s-1s+1)…