The Laplace transform of et is Lſe = . If the Laplace transform of f(t) is F(s) and if U(t) is the unit step function, a shift theorem tells us that L[f(t – b)U(t – b)] = eF(s). From this we can deduce that the inverse s-a transform of F(s) = e4 5 U(t – 4)ešt 5 U(t – 4)e*-4 5 U(t – 4)e(e-4) 5 U(t – 5)e“ o o

Q: Find the Laplace transform for 1) (a) f(t) = t cosh 2t. (b) f(t) = e-4 cos 2t.

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Q: Find the inverse Laplace Transform of: 11 5s 3 1 F(s) s2 + 3 s2 + 9' 5s – 7 s4

A: Use the formulas below to calculate the inverse Laplace transform.

Q: determine the inverse Laplace transform of the given function.

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Q: Find the inverse Laplace transform of F(x) = 4s^2−2s+2/(s2−4)(s)

A: The inverse laplace transform of F(s)=4s2-2s+2s(s2-4)

Q: Find the inverse Laplace transform of a (1+ s2 + a2 Cs le

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Q: Find the inverse Laplace transform of 1 F(x) S- s2 (s + 1)

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s).…

Q: Evaluate the inverse Laplace transform L^-1 { (1 + e^-2s)^2 / (s + 2) }

A: Solution

Q: Find the Inverse Laplace Transform of 10. F (s) 2s+3 s²+4s+13

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Q: Find the inverse Laplace transform of 1 G(s) = s2 – 4s + 5

A: Given,

Q: Find the Laplace transform of e- (s+1)? s-1 (s-1)2 s+1

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Q: determine the inverse Laplace transform of F.

A: Given:

Q: Find the inverse Laplace transform of G(s)=1s2−4s+5.

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Q: Find the inverse laplace transform of the followings; a)  X(s)=(s+2)/(s^2+2s+5)…

A: a) Xs=s+2s2+2s+5 Apply Laplace Inverse transform…

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

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Q: determine the inverse Laplace transform of F.

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Q: F(s) = $+4 5 s² +4s+5 S +

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Q: The Laplace transform of x(t) is X(s). Given x(0)=2 and x'(0)=-1, write an expression for the…

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Q: Find the inverse Laplace transform of: S-3 F(s) = (s-3)2+4 S-2

A: It is known that:

Q: If f(p) is the Laplace transform of f(t) and a>0, then e" f(p) is the Laplace transform of…

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Q: determine the inverse Laplace transform of F.

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Q: In (a)-(e) below, find the Laplace transform of f(t), or he inverse Laplace transform of F(s), as…

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Q: PLS ANSWER BOTH I WILL HELPFUL IF GOOD ANSWER

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Q: Determine the inverse Laplace 2s +3 transform of (s+4)

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Q: If the Laplace transform of a function f(t)is F(s), i.e. if L{f(t)}=F(s), the value of f(t) is…

A: If Lf(t) = F(s) then f(t) = L-1F(s)

Q: Find the inverse Laplace transform of F(s)=2s+3/(s+1)(s2+9)

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Q: -s-1 1. F(s) s2+s-2 2s+5 2. F(s) (s-3)2

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Q: 1 2) F(s)=- s'+4s

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Q: Find the inverse Laplace Transform of: s- 1 (s – 2)(s – 3)(s – 4)

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Q: determine the inverse Laplace transform of F.

A: Let f(t) be the inverse Laplace transform of the given function  Take inverse Laplace transform on…

Q: 1. Deduce the continuous function whose Laplace Transform is 10 F(p) P (p² + 9) 2.Find Р2—ЗР+10 (i)…

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Q: 5s + 1 s2 – 7s + 12 F(s) =

A: To find: Inverse Laplace transform of F(s)=5s+1s2-7s+12.

Q: Determine the inverse Laplace transform of the given function 25 L-1 [s²(s² + 4s + 5)]

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Q: Find the Inverse Laplace transform of F(s) = 1/(s+1)(s^2-1)

A: Given, Fs=1s+1s2-1 This can also be written as, Fs=1s+1s+1s-1…

Q: Find the Laplace transform or the inverse Laplace transform as given L-1[_se¬2s (s² +2s-3. а. 3.

A: To find:  L-1se-2ss2+2s-3

Q: Find the inverse Laplace transform of F(s)=2s+3/(s+1) (s2+9).

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Q: The Laplace transform of the function f(t) = e3+*(2t - e3t)² is: %3D

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Q: Find the laplace transform of a periodic function of a sawtooth below; f(t)=a and t= b, 2b, 3b,and…

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Q: A- Find inverse Laplace transform of: 2e-5S S3

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Q: Find the inverse Laplace transform of the given function. 21 F (s) = (s-2)

A: Given that                    F(s)=2!(s-2)3 We have to find the inverse Laplace transform of the…

Q: find the inverse laplace transform of; a)  (S^2+1)/S(S-1)(S+1)(S-2)

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Q: Find the inverse Laplace transform of 3 F(s) = (8 – 1)(8 – 4)

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Q: gCx-3)= {; +マ ×く3 古xー言×, ×23

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Q: 3s+1 5.) f(s) = s² +6s+13

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Q: Explain why the Laplace transform of = = ₁,t>0 t is not defined for any s, while the Laplace…

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Q: 14. Find the inverse Laplace transform of a) F(s) 2+1 s+25 b) F(s) S(-3)

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Q: Use the First Shift Theorem to find the inverse Laplace transform of s – 3 s2 6s + 20

A: Given:

Q: Find the inverse Laplace transform for-2 -3s e F(s) = s + 5 e 54– 3)u(t – 3) e¯u(t) 0 خيار 2 0 خيار…

A: Let's find.

Q: Find the inverse laplace transform of 2s s2+9

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Q: 1. Find the Laplace transform of f(t) (t-3)u, (t)-(-2)u,(t). (s-3)e 2 s2 +6s +13 2. Find inverse…

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