1- Find the Laplace transform of the following functions a)f(t) = (t² – 3)² (b) f(t) = sin²4t (c)f(t) = e"*sinh5t 2- Find inverse Laplace for the following functions 5s + 1 s² – 25 4s + 32 50 (b) F(s) = s3 (a)F(s) = (c)F(s)= %3D s2 – 16 3- Solve the following differential equations by Laplace transform (a) x/ + 2x = 0 ,x(0) = 1.5 (b) x/l – x - (c) x/ +9x = 10et ,x(0) = 0, x(0) = 0 6x = 0 ,x(0) = 11, x(0)/ = 28 %3D %3D %3D 4- solve the following differential equations (10st< 10 t 2 10 S1 0st<2n t 2 2n (a) x +3x +2x = g(t) = { ,x(0) = 0,x(0) = 0 %3D %3D %3D %3D (b) x + x = g(t) = {'o" ,x(0) = 0, x(0)/ = 0 %3D %3D (c) x// +x = 8(t- 3) ,x(0) = 0, x(0)/ = 0 %3D 5- Find (a)8(g(t))tf g(t)has pertod 3 g(t) - (1 0st<2 lo 2 st<3 (b) 1 Isinat (c) = e' + e-t

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: e-2t cos 3t cOS

A: The given question is related to Laplace Transform. The solution is explained below.

Q: 1) Find the inverse Laplace transform of the following: a) L-1 s+1 ans:A = , B=- e* -e s2-7s+6. 5' 5…

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

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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)

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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: 10. Find the inverse Laplace transform of the function 1 1 F(s) (s – 1)(s – 2) " (s – 7)(s – 8)(s –…

A: F(s)=1(s-1)(s-2)+1(s-7)(s-8)(s-9)+1(s-5)(s-6)2+1(s-5)2(s-6)2+3s(s2+1)(s2+4)…

Q: 7. A damping system with a negligibly small spring constant is modelled by x' +bx' = a e1 with…

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Q: B: Find Laplace Transform of f(t)= cos3t By DEF.

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Q: 2s – 1 (a) Determine the inverse Laplace transform of F(s) s2 – 4s + 6 |

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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: 13. ) Find the Laplace transform of a) f) = 3e-t + 2 cos(t) – 5t3/2

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Q: 14. Find the inverse Laplace transform of 2s+1 a) F(s) : s2+25

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Q: 1) Find the Laplace transform of the following function: f(t) = e-12t (3 cosh (3t) — 3 sin(12t)) —…

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Q: 1- Determine the Inverse Laplace transform for -2s²-9s +11 1 (S-2) (s + 3) (s + 1) O Option 1 L-1…

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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: (A) Find Laplace transform of the function : f(t)=1 sin(2t+) cos(21-7)

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Q: 1 5. If the Laplace transform of f(t) = , find F(4s) %3D

A: We have given that , Laplace transform of , f(t)  is e1ss. We need to find  ,  F(4s). We know that ,…

Q: Find inverse Laplace transform of the function 7s – 1 F(s) %3D (s + 1)(s + 2)(s - 3) |

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Q: 7s2 – 3s + 26 F(s) (8 – 1)(s² + 9)

A: Explanation of the solution is given below...

Q: 1) Find the inverse Laplace transform of the following: s+1 а) L-1 [s²-7s+6) ans: A = B=- 7 | 5' 5…

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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: 5s – 11 Find the inverse Laplace transform f(t) = L- {F(s)} of the function F(s) %3D s2 - 4s + 13

A: Use laplace transforms form

Q: Consider the IVP: y" - y' + 2y = 8sin(2t) - 8, with y(0) = -2, y'(0) = -4. Solve the IVP by using…

A: Given IVP is y''-y'+2y=8sin2t-8              (i) With y0=-2, y'0=-4 Taking Laplace transformation of…

Q: 1. Show that the function 2t et cos (et“) is not of exponential order, however its Laplace transform

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Q: 14. Find the inverse Laplace transform of 2s+1 a) F(s) s²+25

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

Q: 2. Use the Laplace Transform table to find Laplace Transform of a) f(t) = sin 2t b) f(t) = e-2t cos…

A: Solution-

Q: (2) Find Inverse Laplace transform for; 1 1-F(s)= s(s +1) 3 2-F(s)=- s' +4

A: We need to find the inverse Laplace transform. Part(1) We have 1ss+1 We use partial decomposition.…

Q: 10s – 3 - Find the inverse Laplace transform of F(s) s2 – 4 - 17 O f) 23 -2t -e 4 23 4 17 + 4 -2t…

A: I have stated the used formulas in the solution

Q: 2s+1 Determine the Inverse Laplace Transform of: L{; (s²+4s+4)(s2-4)*

A: Let us assume L{f(t)}=F(s) Laplace transform of some unknown function f(t) is given…

Q: Which of the following is the Laplace transform of the solution to the initial value problem x" + a'…

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Q: 1: Find inverse Laplace transform of the following functio 1 2) F(s)=- 3 s'+4s

A: find the inverse laplace transform of the given function

Q: (a)Find the inverse Laplace transforms of F(s) = -2s3+9s²+88–12 %3D (b)Using the definition of the…

A: To find the inverse Laplace transform of the below function.

Q: Find the inverse Laplace transform of 7s + 3 s > 0 s2 + 17

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Q: Find the inverse Laplace transform of 5s + 1 F(s) = s2 – 7s + 12

A: F(s)=5s+1s2-7s+12       =5s+1s2-3s-4s+12       =5s+1s(s-3)-4(s-3)       =21(s-3)-16(s-4)(s-3)(s-4)…

Q: Give the Laplace transform of -2x 0Sx and x < 3 f(x) = 4 3<x -3s 27 20 O F(s) = -- b) O F(s) = - -3s…

A: Solution :-

Q: 7 Find the inverse Laplace transform of using Residue theorem. (s+3)(s²+5s+6)

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Q: 5 The inverse Laplace transform of the function sin(2t) (A) 1 – 2 sinh(2t) (B) t- 2 sin(2t) (C) t- 2…

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Q: 1. Find the Laplace transform of the following: a) f(x) = x5 e-* b) f(x) = x3 + 3 cos2x 2. Find the…

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Q: 1 Find the Inverse Laplace Transform of s2+2s+ 10 (A -e "cos3t 3 1 B -e -'sin9t 3 3r -e"cost D -e…

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Q: Find laplace transform of x" + 3x' + 2x = t(e^(-t)) Where x'(0) = 0 , x(0) = 1

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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: 1. Find the Laplace transform of f(t) = (t-3)u,(t)-(-2)u,(t). (s-3)e2 s +6s +13 2. Find inverse…

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Q: 3.15 - Find the inverser Laplace transform of the following functions: 2s4+9s³+15s²+s +2 h. G(s) =…

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Q: 1. Determine the inverse Laplace transform of the function below. 10 G(s) = (s + 1)(s2 + 4s + 13) 2.…

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Q: 4. Find the Laplace transforms of a) Sinh 3t cos²t | cos (t-2n/3), b) t > 2t/3 14, c) t'e'sin6t. t <…

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

A: Find the inverse Laplace  as per our company guidelines we are supposed to answer ?️only first 3️⃣…

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)…