-60 The inverse Laplace transform of (s+6)³ is btcet, where b, c and w are constants and t represents time.

Q: 2 f(x) = (ae-4x + be-3x + ce-2x) if x > 0

A: The given problem is to find the Fourier cosine transform of the given function and also find the…

Q: 7. Q(s) = S s² +64

A: GivenA Laplace domain function is defined as followsAimTo find the inverse Laplace transform of the…

Q: s+7 s2-3s-10

A: If the Laplace transformation of the function: y(t) is Y(s), then it can be written that Ly(t)=Y(s)…

Q: L-1{ 1 (s2+1)(s2+4s+8)

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Q: 2. F(s): = 3s² +5s-4 S4

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

A: Given the expression of the inverse Laplace expression is: F(s)=1(s-2)(s-4)(s-8) Use partial…

Q: 2s2 + 5s – 4 3. s3 + s² – 2s -

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Q: 25 s3(s2 +4s+5)

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Q: 12 d*x(t) 5 dt3 d²x(t) dt² + 5x(t) = 3cos(2t) d²x(0) 2, dt2 dx(0) 1, dt x(0) = 1 3s2 + 5s + 1 X(s) :…

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Q: a k 2 + k² S 2 + k² k

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Q: f(t) = e-2tsin²tcos²t

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Q: sin 3t 4. f (t) t

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Q: F(s)= (s +1)es» s²(s + 2) -5s

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Q: 5. 6. 7. 6s²-13s+2 s(s-1)(s-6) s+11 (s-1)(s+3) 58² +34s+53 (s+3)² (s+1)

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Q: L{t – e-3t} = + s-3 L{t – e-3t} = =-- I. II. s-3 L{t – e-3t} = +3 L{t – e-3t} = III. IV. %3D s+3

A: We know the Laplace transforms Ltn=n!sn+1, s>0 L ea t =1s-a, s>a Now, Lt-e-3t=Lt-Le-3t L t…

Q: Find the Inverse Laplace Transform.

A: The given function is Fs=10s-48s-53. Let 10s-48s-53=As-5+Bs-52+Cs-53. Remove the fraction and obtain…

Q: 10s2+5s+4 F(s) (s³–6s²+11s-6)(s³)

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Q: 3s-2 2s2-4s+2

A: The given function is                                             3s-22s2-4s+2

Q: Find the Laplace transforms F(s) of the following functions: a. 4t+3 b. 5e²¹ +4e-3t c. 3t² +8 sin 5t

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Q: Find the inverse Laplace transform of 7s (3s²+75)²

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Q: f(t) = t²sinh3t

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Q: 6s + 15 s >0 s2 + 25

A: The given function is    9s+15s2+25        s>0     we have to find inverse Laplace Transform of…