Compute the Laplace Transform of the given functions: First, rewrite in terms of step functions! To do this at each step you 'add the jump'. That is, if the formula changes from gi(t) to 92(t) at t=c, then you will have a term of the form u(t) (g(t)- gi(t)) in the function. Second, use L[u(t)f(t-c)}=eC{f(t)}. Another way to write this is C{u,(t)f(t)}=eC{f(t+c)}. Thus, you 'pull out' (t) and write e out in front. At the same time you replace t' with t+e' and find the Laplace function of the new expression. 1. f(t) 0,0 ≤ t < 6: ,t≥ 6. - {% 3

Q: Find the Laplace transform of each function: y = S(x)

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Q: Get the function in algebraic form, state its representation in terms of the function unit step and…

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Q: Find the inverse Laplace transform of the following functions (a). F(s) 2 = s²+3s-4 2s+4 (b). F(s) =…

A: To solve the given problems, we need to find the inverse Laplace transform of the given functions.…

Q: Find the inverse Laplace transform of the function as + b H(s) = (s – a)2 + 32 °

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Q: Find the inverse Laplace transform of -8s F(s) = e s² - 18 - 12 f(t) = =. (Use step(t-c) for uc(t).)

A: The given problem is to find the Inverse Laplace transform of the given function F(S) to find the…

Q: a) Find the Fourier transform of 4 f(t) = e tu(t) + -tu(t) + ²9.

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Q: Calculate the Inverse Laplace transform of the following. Please write down all the steps of your…

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Q: b) Find the inverse Laplace transform of the following function: 3s +6 F(s) = s² +9s + 5.

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Q: Find the Laplace transform of the function f(t)= (5e/t+4t)using the table of known as2+bs+c…

A: We first find Laplace transform and then comparing we find the value of c.

Q: Find the inverse Laplace Transform of F(s) 2s2 + s -3 F(s) = s4 +3s2 + 2

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Q: Find the inverse Laplace transform L-1{F(s)} of the function F(s) = - 4 (8 – 4)³ NOTE: The ansuwer…

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Q: Use Laplace transform to solve for f(t): (t-7)S(T)dr=t.

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Q: Find the Fourier Transforms of the indicated function: f (x) = e-3x for x > 0 and f (x) = e2x for x…

A: We have,fx=e-3xx&gt;0e2xx&lt;0 To Do: Find the Fourier Transform of the given function.

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

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Q: * + 3x + 6x = 0, x(0) = 0, x(0) = 3, x(t) =?

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Q: = Find the inverse Laplace transform f(t) = £¹{F(s)} of the function F(s) = f(t) = = L 6s+2 s² + 100…

A: The function: Fs=6s+2s2+100. We have to find the inverse Laplace transform of the given function.

Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: a cylindrical swimming pool contains about 972 cubic feet of water. What is the appropriate diameter…

A: Given that a cylindrical swimming pool contains about 972 cubic feet of water. This implies the…

Q: 5. Find the inverse Laplace transform of the function as + b H(s) : (8 – a)2 + B2"

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Q: 8 Find the inverse Laplace transform of F (s) = f (t) = 8"H(t) (Write eab as exp(a*b)). %3| ||

A: We have to find laplace inverse of F(s)

Q: 6. Find the inverse Laplace transform of the function (B² – a²)(as + b) (s² + a²)(s² + B²)" I(s) =

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Q: Find the Fourier transform $\tilde{f}(p)$ of the function 4x²e-5¹ for x ≥ 0 for x < 0. f(x) = {…

A: fx=4x2e-5xfor x≥00for x&lt;0

Q: Show that the sequence {a_n} is a solution of the recurrence relation a_n = -3a_(n-1) + 4a_(n-2) if…

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Q: B- Find Inverse Laplace transform of the following functions F(s)= 2s-7 (s+ 6)(s² + 4) G(s) = s(s² +…

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Q: Find the Fourier Transforms of the indicated function: f (x) = xe-|x|

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Q: 1 F(s) : (s-2)(s-4)(s-8)

A: Use the Laplace table.

Q: Find the inverse Laplace transform of f(t) F(s) = = help (formulas) (Notation: write u(t-c) for the…

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Q: Determine the inverse laplace transform of this function: 8(s + 1)(s + 3) s(s + 2)(s + 4)

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