4. Evaluate each of the following expressions, where u, & and L denote, respectively, the Heaviside function (or unit step function), the Dirac delta function and the Laplace transform. Remember to show your work! a. f(3), where f(t) = (t- 1)u(t- 1) +4u(t-2) b. (3x- 5)6(x+ 1) dr c. L{-14u(t-3) + 1}

Q: 13. Find the Laplace transform of each of the following functions: (a) t (b) t² (c) t", where n is a…

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Q: Determine the Laplace transform of the following 5t3 + 4t2-3

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Q: Express the given function in terms of the unit step function and find the Laplace transform. F(s) =…

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Q: 8. f(t)=t"² 7/2

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Q: Find the inverse Laplace transform L-{F(s)} of the function 5(s – 8)e-8s F(s) s2 – 16s + 145 NOTE:…

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Q: S F(s) = (s + 3)(s² + 4),

A: The solution is given as

Q: A. Find the Laplace transform of each given expression (5 (2) i++ t sin(3t) + y, where x = z(t), a…

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Q: 8. Find the inverse Laplace transform of the given function: 8s +7 F(s) = s2 +8s + 20

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Q: Find the inverse Laplace transform of (s² + 4) s(s² +16)

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Q: 3s Find L-1 s2 + 2s + 5

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Q: 7. Find the inverse Laplace transform for the F(s): (S-2)e-2s 4s + 3 5² Hint: You may need unit step…

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Q: Q5: Express the following function in terms of units step function and find its Laplace Transform.…

A: To find- Express the following function in terms of unit step function and fins its Laplace…

Q: Q2. Fine the inverse of two Laplace transform for follo a. L-1 3S3+3S² + S S²+S-6

A: The given problem is to find the Inverse Laplace transform of the given function. Given function,…

Q: 4. Find the inverse Laplace transform of the function as +b s2 + 32" G(s) : %3|

A: We use the table of inverse Laplace transform to solve the given question.

Q: Find the general solution of the following differential equation. 1 y" + 1 h. In I

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Q: s2 + 6s + 8 G(s) = s4 + 8s2 + 16° xnlanation calculation IS we

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Q: Q9. Use Laplace transform to solve the ODE. X-4x +3x =-8cos4t, x(0) =0, x(0) = 0 %3D

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Q: 2. Find the inverse Laplace transform of the following function -3s F(s) a 1 (s2 –6s+25) + + s-b…

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Q: Relate the concept of Laplace Transform to solve the following problems. A. Compute the Laplace…

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Q: t < 0; 4. f(t){t, 0 <t < 4; t 2 4. rof (6,

A: As per the company rule, we are supposed to do only one problem. Kindly repost the second problem.

Q: Use the Laplace transform table and the linearity of the Laplace transform to determine the…

A: Given: L9e-5t-t3+7t-8. To Do: We have to determine the formula for the Laplace transform.

Q: Q4.A. Find Laplace Transform for the signal f(t)= t sin 2t

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